Beautifully presented, 21 Mar 2007
Its a real pleasure to see a clearly laid out undergraduate-oientated introduction to GR hich is predominantly aimed at those with a mathematical background. Consequently it is uncluttered and easy to follow.Most importantly the guidance notes on the solutions are a dream especially for students self-studying who do not have access to a tutor.
I can see myself using this and referring to it frequently.Definitely an instant favourite. A great start point for further and higher studies in GR and theoretical/mathematical physics.

Beautifully presented, 21 Mar 2007
Its a real pleasure to see a clearly laid out undergraduate-oientated introduction to GR hich is predominantly aimed at those with a mathematical background. Consequently it is uncluttered and easy to follow.Most importantly the guidance notes on the solutions are a dream especially for students self-studying who do not have access to a tutor.
I can see myself using this and referring to it frequently.Definitely an instant favourite. A great start point for further and higher studies in GR and theoretical/mathematical physics.




Very good textbook, clearly aimed at undergraduates., 05 Nov 2003
This is one of the clearest and easiest to follow textbooks I have had the pleasure to use in the last year. It happened to be one of the recommended texts for our 2nd year "Geometry of Surfaces Course".

It is well written and fairly well structured, providing a consistently flowing and logical exposition of the material. There are a plenty of diagrams and worked out examples, so one can easily see whether he's on the ball or not. Apart from worked out exaples directly in the text, there is a wealth of exercies, with solutions (or major hints) at the back. The exercies are almost worth the price of the book by themself, starting from basic ones, checking that one understands definitions, followed by more difficult ones outlining the subtler points of the subject and a couple of rather involved ones; ones which it is easy to spend a whole afternoon with.

The author does a good job at pointing the diffucult parts of proofs and constructions. The style is very enthusiastic, which might help motivating the reader. The proofs are sometimes a bit too fast paced for someone who might not be as quick witted as the author when it comes to differetial calculus. I did find certain steps not obvious the first time round. A second or third reading (plus trying to work out the steps on a paper) helps a lot.

What is rather important to know, before buying, is that the book is only concerned with curves and surfaces in 3 dimensional euclidean space. The approaches taken here would not, very often, generalise to higher dimensional cases. This means that the material is easily accesible to begginers. At the same time, it is not for people who are after an introduction to coordinate free geometry and manifolds.

Topics covered here include: curvature, smooth surfaces, tangents normals & orientability, first & second fundametal forms, curvatures of surfaces, gaussian curvature, geodesics, and the amazing Gauss-Bonet theorem. By the time Gauus-Bonnet theorems are discussed, I had the feeling that the proofs are not as detailed and rigorous as they could be. On the other hand this makes them easier to follow and one is not overwhelmed by techicalities.

So why not give it 5? I don't know, maybe there are other better books out there, maybe I'm just not too keen on differential geometry in general. I guess I might have given it 5, but then maybe Prof. Pressley won't feel like improving this great book and that would be a shame.

Beautifully presented, 21 Mar 2007
Its a real pleasure to see a clearly laid out undergraduate-oientated introduction to GR hich is predominantly aimed at those with a mathematical background. Consequently it is uncluttered and easy to follow.Most importantly the guidance notes on the solutions are a dream especially for students self-studying who do not have access to a tutor.
I can see myself using this and referring to it frequently.Definitely an instant favourite. A great start point for further and higher studies in GR and theoretical/mathematical physics.




Very good textbook, clearly aimed at undergraduates., 05 Nov 2003
This is one of the clearest and easiest to follow textbooks I have had the pleasure to use in the last year. It happened to be one of the recommended texts for our 2nd year "Geometry of Surfaces Course".

It is well written and fairly well structured, providing a consistently flowing and logical exposition of the material. There are a plenty of diagrams and worked out examples, so one can easily see whether he's on the ball or not. Apart from worked out exaples directly in the text, there is a wealth of exercies, with solutions (or major hints) at the back. The exercies are almost worth the price of the book by themself, starting from basic ones, checking that one understands definitions, followed by more difficult ones outlining the subtler points of the subject and a couple of rather involved ones; ones which it is easy to spend a whole afternoon with.

The author does a good job at pointing the diffucult parts of proofs and constructions. The style is very enthusiastic, which might help motivating the reader. The proofs are sometimes a bit too fast paced for someone who might not be as quick witted as the author when it comes to differetial calculus. I did find certain steps not obvious the first time round. A second or third reading (plus trying to work out the steps on a paper) helps a lot.

What is rather important to know, before buying, is that the book is only concerned with curves and surfaces in 3 dimensional euclidean space. The approaches taken here would not, very often, generalise to higher dimensional cases. This means that the material is easily accesible to begginers. At the same time, it is not for people who are after an introduction to coordinate free geometry and manifolds.

Topics covered here include: curvature, smooth surfaces, tangents normals & orientability, first & second fundametal forms, curvatures of surfaces, gaussian curvature, geodesics, and the amazing Gauss-Bonet theorem. By the time Gauus-Bonnet theorems are discussed, I had the feeling that the proofs are not as detailed and rigorous as they could be. On the other hand this makes them easier to follow and one is not overwhelmed by techicalities.

So why not give it 5? I don't know, maybe there are other better books out there, maybe I'm just not too keen on differential geometry in general. I guess I might have given it 5, but then maybe Prof. Pressley won't feel like improving this great book and that would be a shame.

A comprehensive intro to Differential Geometry, 02 Mar 2001
It is a bit informal exposition in comparison with other more mathematical rigorous titles. Definitions of difficult concepts like tensors or manifolds are very accessible and the same to differential forms. It is suitable for any first course in modern geometry applied to physics, above all in relativity theory. As a suggest I think the Riemannian geometry chapter should be increased.

excellent, 13 Nov 1999
This book provides a unique introduction to differential geometry and its applications. The only prerequisites are a general knowledge of algebra and calculus. Applications in areas such as mechanics, thermodynamics, electromagnetism and especially general relativity are explained in detail. An almost essential book for the advanced undergraduate or beginning graduate student of theoretical or mathematical physics.

Beautifully presented, 21 Mar 2007
Its a real pleasure to see a clearly laid out undergraduate-oientated introduction to GR hich is predominantly aimed at those with a mathematical background. Consequently it is uncluttered and easy to follow.Most importantly the guidance notes on the solutions are a dream especially for students self-studying who do not have access to a tutor.
I can see myself using this and referring to it frequently.Definitely an instant favourite. A great start point for further and higher studies in GR and theoretical/mathematical physics.




Very good textbook, clearly aimed at undergraduates., 05 Nov 2003
This is one of the clearest and easiest to follow textbooks I have had the pleasure to use in the last year. It happened to be one of the recommended texts for our 2nd year "Geometry of Surfaces Course".

It is well written and fairly well structured, providing a consistently flowing and logical exposition of the material. There are a plenty of diagrams and worked out examples, so one can easily see whether he's on the ball or not. Apart from worked out exaples directly in the text, there is a wealth of exercies, with solutions (or major hints) at the back. The exercies are almost worth the price of the book by themself, starting from basic ones, checking that one understands definitions, followed by more difficult ones outlining the subtler points of the subject and a couple of rather involved ones; ones which it is easy to spend a whole afternoon with.

The author does a good job at pointing the diffucult parts of proofs and constructions. The style is very enthusiastic, which might help motivating the reader. The proofs are sometimes a bit too fast paced for someone who might not be as quick witted as the author when it comes to differetial calculus. I did find certain steps not obvious the first time round. A second or third reading (plus trying to work out the steps on a paper) helps a lot.

What is rather important to know, before buying, is that the book is only concerned with curves and surfaces in 3 dimensional euclidean space. The approaches taken here would not, very often, generalise to higher dimensional cases. This means that the material is easily accesible to begginers. At the same time, it is not for people who are after an introduction to coordinate free geometry and manifolds.

Topics covered here include: curvature, smooth surfaces, tangents normals & orientability, first & second fundametal forms, curvatures of surfaces, gaussian curvature, geodesics, and the amazing Gauss-Bonet theorem. By the time Gauus-Bonnet theorems are discussed, I had the feeling that the proofs are not as detailed and rigorous as they could be. On the other hand this makes them easier to follow and one is not overwhelmed by techicalities.

So why not give it 5? I don't know, maybe there are other better books out there, maybe I'm just not too keen on differential geometry in general. I guess I might have given it 5, but then maybe Prof. Pressley won't feel like improving this great book and that would be a shame.

A comprehensive intro to Differential Geometry, 02 Mar 2001
It is a bit informal exposition in comparison with other more mathematical rigorous titles. Definitions of difficult concepts like tensors or manifolds are very accessible and the same to differential forms. It is suitable for any first course in modern geometry applied to physics, above all in relativity theory. As a suggest I think the Riemannian geometry chapter should be increased.

excellent, 13 Nov 1999
This book provides a unique introduction to differential geometry and its applications. The only prerequisites are a general knowledge of algebra and calculus. Applications in areas such as mechanics, thermodynamics, electromagnetism and especially general relativity are explained in detail. An almost essential book for the advanced undergraduate or beginning graduate student of theoretical or mathematical physics.

One of the best places to start..., 08 Oct 2006
Nakahara's book is one of the best introductions to geometry and topology that I have read. I constantly use the book as the starting place for just about any topic in geometry and topolgy.

After reading the book you will not be able to jump straight into research work, but it does bridge the gap between more advanced texts and papers.

Everybody should have a copy.

Good graduate intro to Differential Geom, 01 Sep 2005
To complete this book, there should be a section on general curvilinear coordinate transformations, the ultimate foundation of tensor calculus.This is a defficiency this book shares with many differential geometry texts.But maybe this can be forgiven at graduate level, for which this book is a decent pedagogical text- if a little terse at times.

The book begins with a survey of those areas of physics to which diff geom are applied , then develops some topology, and goes on to a comprehensive discussion of the theory of finite dimensional manifolds-including a chapter on complex manifolds.You will learn basic exterior calculus, lie derivatives and covariant derivatives , and so on.A first choice for those who have had a little preparation at undergraduate level.

Beautifully presented, 21 Mar 2007
Its a real pleasure to see a clearly laid out undergraduate-oientated introduction to GR hich is predominantly aimed at those with a mathematical background. Consequently it is uncluttered and easy to follow.Most importantly the guidance notes on the solutions are a dream especially for students self-studying who do not have access to a tutor.
I can see myself using this and referring to it frequently.Definitely an instant favourite. A great start point for further and higher studies in GR and theoretical/mathematical physics.




Very good textbook, clearly aimed at undergraduates., 05 Nov 2003
This is one of the clearest and easiest to follow textbooks I have had the pleasure to use in the last year. It happened to be one of the recommended texts for our 2nd year "Geometry of Surfaces Course".

It is well written and fairly well structured, providing a consistently flowing and logical exposition of the material. There are a plenty of diagrams and worked out examples, so one can easily see whether he's on the ball or not. Apart from worked out exaples directly in the text, there is a wealth of exercies, with solutions (or major hints) at the back. The exercies are almost worth the price of the book by themself, starting from basic ones, checking that one understands definitions, followed by more difficult ones outlining the subtler points of the subject and a couple of rather involved ones; ones which it is easy to spend a whole afternoon with.

The author does a good job at pointing the diffucult parts of proofs and constructions. The style is very enthusiastic, which might help motivating the reader. The proofs are sometimes a bit too fast paced for someone who might not be as quick witted as the author when it comes to differetial calculus. I did find certain steps not obvious the first time round. A second or third reading (plus trying to work out the steps on a paper) helps a lot.

What is rather important to know, before buying, is that the book is only concerned with curves and surfaces in 3 dimensional euclidean space. The approaches taken here would not, very often, generalise to higher dimensional cases. This means that the material is easily accesible to begginers. At the same time, it is not for people who are after an introduction to coordinate free geometry and manifolds.

Topics covered here include: curvature, smooth surfaces, tangents normals & orientability, first & second fundametal forms, curvatures of surfaces, gaussian curvature, geodesics, and the amazing Gauss-Bonet theorem. By the time Gauus-Bonnet theorems are discussed, I had the feeling that the proofs are not as detailed and rigorous as they could be. On the other hand this makes them easier to follow and one is not overwhelmed by techicalities.

So why not give it 5? I don't know, maybe there are other better books out there, maybe I'm just not too keen on differential geometry in general. I guess I might have given it 5, but then maybe Prof. Pressley won't feel like improving this great book and that would be a shame.

A comprehensive intro to Differential Geometry, 02 Mar 2001
It is a bit informal exposition in comparison with other more mathematical rigorous titles. Definitions of difficult concepts like tensors or manifolds are very accessible and the same to differential forms. It is suitable for any first course in modern geometry applied to physics, above all in relativity theory. As a suggest I think the Riemannian geometry chapter should be increased.

excellent, 13 Nov 1999
This book provides a unique introduction to differential geometry and its applications. The only prerequisites are a general knowledge of algebra and calculus. Applications in areas such as mechanics, thermodynamics, electromagnetism and especially general relativity are explained in detail. An almost essential book for the advanced undergraduate or beginning graduate student of theoretical or mathematical physics.

One of the best places to start..., 08 Oct 2006
Nakahara's book is one of the best introductions to geometry and topology that I have read. I constantly use the book as the starting place for just about any topic in geometry and topolgy.

After reading the book you will not be able to jump straight into research work, but it does bridge the gap between more advanced texts and papers.

Everybody should have a copy.

Good graduate intro to Differential Geom, 01 Sep 2005
To complete this book, there should be a section on general curvilinear coordinate transformations, the ultimate foundation of tensor calculus.This is a defficiency this book shares with many differential geometry texts.But maybe this can be forgiven at graduate level, for which this book is a decent pedagogical text- if a little terse at times.

The book begins with a survey of those areas of physics to which diff geom are applied , then develops some topology, and goes on to a comprehensive discussion of the theory of finite dimensional manifolds-including a chapter on complex manifolds.You will learn basic exterior calculus, lie derivatives and covariant derivatives , and so on.A first choice for those who have had a little preparation at undergraduate level.

An Excursion into the Realm of Differential Geometry, 29 Feb 2004
My first encounter with this book was during the academic year of 2000-2001, when it was used as the main text for an upper division course on differnetial geometry, at one of the University of California campuses . The class for me --taught by a distinguished scholar-- was only meant to be a brief excursion into the realm of continuous math, beyond analysis and topology. After finishing the class however, I decided to change direction and as time went on, I drifted more and more towards geometry as the field of further concentration. Before we proceed further, let me note that one main complaint that's rather well-known about this text is the issue of numerous typo's therein. What many may not know however is that the first edition from 1966 does not contain any noticeable typo's, unfortunately somehow all of them found their way in the 1997's second edition. This is very likely because of careless typesetting, but one good news is that many of these are noted on the errata sheet available from the author's UCLA web site. Moreover, the book uses a cumbersome section numbering format, and to make things worse, in quite a few places the reader is referred to one or more previous sections. This serves to disrupt the flow of reading by taking up some time and effort to locate the correct previous page number which is being referenced.

Within the eight chapters of the book (seven chapters in the first edition), the reader is first introduced to some preliminaries such as tangent vectors, directional derivatives, and differential forms. In chapter two, the author presents the Frenet frame formulas, covariant derivatives, connection forms, and Cartan's structural equations, which are generalizations of the Frenet frame formulas for surfaces. In chapters three and four, there is a healthy dose of Euclidean geometry and calculus on surfaces. In chapter five, discussion shifts to the study of the shape operators and normal and Gaussian curvatures, where also some useful computational examples have been presented. Geometry of surfaces is the subject of chapter six, where the crucial Gauss' egregium theorem and some global theorems are also discussed, and in chapter seven students are introduced to the basics of the Riemannian geometry, culminating in the famous Gauss-Bonnet theorem. In chapter eight (which is highly topological), the concepts of geodesics, complete surfaces, covering spaces, Jacobi fields, conjugate points, and a couple of constant curvature theorems for surfaces are explored. The appendices include help on using popular computer algebra systems, and another appendix providing solutions to most of the odd-numbered exercises in the book.

Again, looking on the downside, the book lacks a discussion of several essential tools, for example, the Schwarz-Christoffel symbols, tensors, and Lie derivatives, as well as some other important topics such as the first and second fundamental forms, and parallel translation, which only show up in the exercises. Then again, perhaps to keep the level of exposition elemantary and the size limited to less than 500 pages, Dr. O'Neill has preferred to skip some topics. One remedy is to back this text up with Manfredo Do Carmo's 1976 classic, which is mathematically more rigorous, and covers more of the above-mentioned topics (be aware though that Do Carmo is less accessible for the beginning students). Afterwards, one can certainly continue the study of the essentials by reading other advanced books such as Barrett O'Neill's (obscure) graduate-level 1983 treatise on Applications of the Semi-Riemannian Geometry to Relativity, or William Boothby's "An Introduction to Differentiable Manifolds and Riemannian Geometry". One other underrated source which is worthwhile to look into is Richard W. Sharpe's "Differential Geometry: Cartan's Generalization of Klein's Erlangen Program", from the Springer-Verlag GTM series.

OK for undergrads, if you can put up with the typos, 07 May 1999
This book is, I suppose, an acceptable elementary introduction to the topic. However, I found that several important proofs were annoyingly incomplete, with the tag "the proof is too difficult to go into here." Many times, the only ingredient needed to complete the proof is the Inverse Function Theorem or the Implicit Function Theorem, which students taking differential geometry should know. Also, and more significantly, the exercises are riddled with typos; some are minor, others make the exercise incomprehensible. A final minor quibble is that the author uses a cumbersome numbering system for his sections. In sum: If your mathematical background is at least as strong as that of a senior honors undergraduate mathematics major, look elsewhere (perhaps "Differential Geometry of Curves and Surfaces," by do Carmo). If not, and you still would like an introduction to the field, this book may foot the bill--just beware of the typos in the exercises!

Excellent book for upper undergrad math student., 27 Aug 1998
Because this book has made it into a 2nd edition should say enough (in this area of study). The book has wonderful notation that makes sense and problems that start out easy and go up from there! There is also extensive use of math computer programs (mathmatica & maple) for problems and examples. Wonderful book & one of my favorite undergrad texts!

Beautifully presented, 21 Mar 2007
Its a real pleasure to see a clearly laid out undergraduate-oientated introduction to GR hich is predominantly aimed at those with a mathematical background. Consequently it is uncluttered and easy to follow.Most importantly the guidance notes on the solutions are a dream especially for students self-studying who do not have access to a tutor.
I can see myself using this and referring to it frequently.Definitely an instant favourite. A great start point for further and higher studies in GR and theoretical/mathematical physics.




Very good textbook, clearly aimed at undergraduates., 05 Nov 2003
This is one of the clearest and easiest to follow textbooks I have had the pleasure to use in the last year. It happened to be one of the recommended texts for our 2nd year "Geometry of Surfaces Course".

It is well written and fairly well structured, providing a consistently flowing and logical exposition of the material. There are a plenty of diagrams and worked out examples, so one can easily see whether he's on the ball or not. Apart from worked out exaples directly in the text, there is a wealth of exercies, with solutions (or major hints) at the back. The exercies are almost worth the price of the book by themself, starting from basic ones, checking that one understands definitions, followed by more difficult ones outlining the subtler points of the subject and a couple of rather involved ones; ones which it is easy to spend a whole afternoon with.

The author does a good job at pointing the diffucult parts of proofs and constructions. The style is very enthusiastic, which might help motivating the reader. The proofs are sometimes a bit too fast paced for someone who might not be as quick witted as the author when it comes to differetial calculus. I did find certain steps not obvious the first time round. A second or third reading (plus trying to work out the steps on a paper) helps a lot.

What is rather important to know, before buying, is that the book is only concerned with curves and surfaces in 3 dimensional euclidean space. The approaches taken here would not, very often, generalise to higher dimensional cases. This means that the material is easily accesible to begginers. At the same time, it is not for people who are after an introduction to coordinate free geometry and manifolds.

Topics covered here include: curvature, smooth surfaces, tangents normals & orientability, first & second fundametal forms, curvatures of surfaces, gaussian curvature, geodesics, and the amazing Gauss-Bonet theorem. By the time Gauus-Bonnet theorems are discussed, I had the feeling that the proofs are not as detailed and rigorous as they could be. On the other hand this makes them easier to follow and one is not overwhelmed by techicalities.

So why not give it 5? I don't know, maybe there are other better books out there, maybe I'm just not too keen on differential geometry in general. I guess I might have given it 5, but then maybe Prof. Pressley won't feel like improving this great book and that would be a shame.

A comprehensive intro to Differential Geometry, 02 Mar 2001
It is a bit informal exposition in comparison with other more mathematical rigorous titles. Definitions of difficult concepts like tensors or manifolds are very accessible and the same to differential forms. It is suitable for any first course in modern geometry applied to physics, above all in relativity theory. As a suggest I think the Riemannian geometry chapter should be increased.

excellent, 13 Nov 1999
This book provides a unique introduction to differential geometry and its applications. The only prerequisites are a general knowledge of algebra and calculus. Applications in areas such as mechanics, thermodynamics, electromagnetism and especially general relativity are explained in detail. An almost essential book for the advanced undergraduate or beginning graduate student of theoretical or mathematical physics.

One of the best places to start..., 08 Oct 2006
Nakahara's book is one of the best introductions to geometry and topology that I have read. I constantly use the book as the starting place for just about any topic in geometry and topolgy.

After reading the book you will not be able to jump straight into research work, but it does bridge the gap between more advanced texts and papers.

Everybody should have a copy.

Good graduate intro to Differential Geom, 01 Sep 2005
To complete this book, there should be a section on general curvilinear coordinate transformations, the ultimate foundation of tensor calculus.This is a defficiency this book shares with many differential geometry texts.But maybe this can be forgiven at graduate level, for which this book is a decent pedagogical text- if a little terse at times.

The book begins with a survey of those areas of physics to which diff geom are applied , then develops some topology, and goes on to a comprehensive discussion of the theory of finite dimensional manifolds-including a chapter on complex manifolds.You will learn basic exterior calculus, lie derivatives and covariant derivatives , and so on.A first choice for those who have had a little preparation at undergraduate level.

An Excursion into the Realm of Differential Geometry, 29 Feb 2004
My first encounter with this book was during the academic year of 2000-2001, when it was used as the main text for an upper division course on differnetial geometry, at one of the University of California campuses . The class for me --taught by a distinguished scholar-- was only meant to be a brief excursion into the realm of continuous math, beyond analysis and topology. After finishing the class however, I decided to change direction and as time went on, I drifted more and more towards geometry as the field of further concentration. Before we proceed further, let me note that one main complaint that's rather well-known about this text is the issue of numerous typo's therein. What many may not know however is that the first edition from 1966 does not contain any noticeable typo's, unfortunately somehow all of them found their way in the 1997's second edition. This is very likely because of careless typesetting, but one good news is that many of these are noted on the errata sheet available from the author's UCLA web site. Moreover, the book uses a cumbersome section numbering format, and to make things worse, in quite a few places the reader is referred to one or more previous sections. This serves to disrupt the flow of reading by taking up some time and effort to locate the correct previous page number which is being referenced.

Within the eight chapters of the book (seven chapters in the first edition), the reader is first introduced to some preliminaries such as tangent vectors, directional derivatives, and differential forms. In chapter two, the author presents the Frenet frame formulas, covariant derivatives, connection forms, and Cartan's structural equations, which are generalizations of the Frenet frame formulas for surfaces. In chapters three and four, there is a healthy dose of Euclidean geometry and calculus on surfaces. In chapter five, discussion shifts to the study of the shape operators and normal and Gaussian curvatures, where also some useful computational examples have been presented. Geometry of surfaces is the subject of chapter six, where the crucial Gauss' egregium theorem and some global theorems are also discussed, and in chapter seven students are introduced to the basics of the Riemannian geometry, culminating in the famous Gauss-Bonnet theorem. In chapter eight (which is highly topological), the concepts of geodesics, complete surfaces, covering spaces, Jacobi fields, conjugate points, and a couple of constant curvature theorems for surfaces are explored. The appendices include help on using popular computer algebra systems, and another appendix providing solutions to most of the odd-numbered exercises in the book.

Again, looking on the downside, the book lacks a discussion of several essential tools, for example, the Schwarz-Christoffel symbols, tensors, and Lie derivatives, as well as some other important topics such as the first and second fundamental forms, and parallel translation, which only show up in the exercises. Then again, perhaps to keep the level of exposition elemantary and the size limited to less than 500 pages, Dr. O'Neill has preferred to skip some topics. One remedy is to back this text up with Manfredo Do Carmo's 1976 classic, which is mathematically more rigorous, and covers more of the above-mentioned topics (be aware though that Do Carmo is less accessible for the beginning students). Afterwards, one can certainly continue the study of the essentials by reading other advanced books such as Barrett O'Neill's (obscure) graduate-level 1983 treatise on Applications of the Semi-Riemannian Geometry to Relativity, or William Boothby's "An Introduction to Differentiable Manifolds and Riemannian Geometry". One other underrated source which is worthwhile to look into is Richard W. Sharpe's "Differential Geometry: Cartan's Generalization of Klein's Erlangen Program", from the Springer-Verlag GTM series.

OK for undergrads, if you can put up with the typos, 07 May 1999
This book is, I suppose, an acceptable elementary introduction to the topic. However, I found that several important proofs were annoyingly incomplete, with the tag "the proof is too difficult to go into here." Many times, the only ingredient needed to complete the proof is the Inverse Function Theorem or the Implicit Function Theorem, which students taking differential geometry should know. Also, and more significantly, the exercises are riddled with typos; some are minor, others make the exercise incomprehensible. A final minor quibble is that the author uses a cumbersome numbering system for his sections. In sum: If your mathematical background is at least as strong as that of a senior honors undergraduate mathematics major, look elsewhere (perhaps "Differential Geometry of Curves and Surfaces," by do Carmo). If not, and you still would like an introduction to the field, this book may foot the bill--just beware of the typos in the exercises!

Excellent book for upper undergrad math student., 27 Aug 1998
Because this book has made it into a 2nd edition should say enough (in this area of study). The book has wonderful notation that makes sense and problems that start out easy and go up from there! There is also extensive use of math computer programs (mathmatica & maple) for problems and examples. Wonderful book & one of my favorite undergrad texts!

Good, 29 Dec 2001
It's a really clearcut staightforward representation of differential geometry of curves and surfaces. Just like it says. Lots of good stuff in it. Treats Gaussian Curvature well.