In February 2001, scientists at the Los Alamos National Laboratory announced that they had recorded a simple knot untying itself. Crafted from a chain of nickel-plated steel balls connected by thin metal rods, the three-crossing knot stretched, wiggled, and bent its way out of its predicament--a neat trick worthy of an inorganic Houdini, but more, a critical discovery in how granular and filamentary materials such as strands of DNA and polymers entangle and enfold themselves.

A knot seems a simple, everyday thing, at least to anyone who wears laced shoes or uses a corded telephone. In the mathematical discipline known as topology, knots are anything but simple: at 16 crossings of a "closed curve in space that does not intersect itself anywhere", a knot can take one of 1,388,705 permutations, and more are possible. All this thrills mathematics professor Colin Adams, whose primer The Knot Book offers an engaging if often challenging introduction to the mysterious, often unproven, but, he suggests, ultimately knowable nature of knots of all kinds--whether nontrivial, satellite, torus, cable or hyperbolic. As perhaps befits its subject, Adams's prose is sometimes... well, tangled ("A knot is amphicheiral if it can be deformed through space to the knot obtained by changing every crossing in the projection of the knot to the opposite crossing.") but his book is great fun for puzzle and magic buffs, and a useful reference for students of knot theory and other aspects of higher mathematics. --Gregory McNamee

Nope, sorry, found it impenetrable, 05 Jan 2008
I think I need to go away and work at this a bit more. I've come into this from a graph theory module at undergrad level, and a certain amount of abstract algebra at (probably) masters level, but I just haven't managed to break through this yet.

The problem's either with me, or with the exposition. I'm going to have to give it another go.

All the same, it's well and entertainingly written, just that I haven't a clue what it's on about.

book is not that basic, provides direction, 09 Aug 1999
Book was purchased with the intent of getting direction into more complicated areas of knot theory, in particular adjacency matrices and using probability mean functions as a weighting technique of mapping.

searching the net for bookbinder's knot, 04 Aug 1999
trying VERY hard to find a bookbinder's knot "how-to" - help! please. where can i get a diagram so that i might learn? for the purpose of knitting a beaded purse, believe it or not! and need to use bookbinder's knot at edges. thank you.

Excellent undergraduate introduction to subject, 23 Dec 1998
Well-written, a good introduction to a mathematical research topic that requires only high-school level mathematics as background. Includes good applications to biology and chemistry, and written with a friendly, easy-going style.

Nope, sorry, found it impenetrable, 05 Jan 2008
I think I need to go away and work at this a bit more. I've come into this from a graph theory module at undergrad level, and a certain amount of abstract algebra at (probably) masters level, but I just haven't managed to break through this yet.

The problem's either with me, or with the exposition. I'm going to have to give it another go.

All the same, it's well and entertainingly written, just that I haven't a clue what it's on about.

book is not that basic, provides direction, 09 Aug 1999
Book was purchased with the intent of getting direction into more complicated areas of knot theory, in particular adjacency matrices and using probability mean functions as a weighting technique of mapping.

searching the net for bookbinder's knot, 04 Aug 1999
trying VERY hard to find a bookbinder's knot "how-to" - help! please. where can i get a diagram so that i might learn? for the purpose of knitting a beaded purse, believe it or not! and need to use bookbinder's knot at edges. thank you.

Excellent undergraduate introduction to subject, 23 Dec 1998
Well-written, a good introduction to a mathematical research topic that requires only high-school level mathematics as background. Includes good applications to biology and chemistry, and written with a friendly, easy-going style.

A gentle introduction to a complex mathematical topic, 13 Sep 2005
This is an excellent little book. If you've always wondered about knot theory, this provides all that you need to get you hooked on this fascinating topic.

The book explains everything in simple diagrams, and doesn't require any great proficiency in algebra. A geometrical intuition is more important. A number of topics are covered and they are treated independently so that you can dip into the book and just read a chapter without having read the rest.

The main topics covered are:

Knots as atoms. 2d representations of knots and Reidemeister moves. Braids. Invariants: the Conway polynomial; the Jones polynomial. The arithmetic of knots. Recent discoveries.

There are a number of minor mistakes in the book, from typographical errors (an x in the wrong place) to a wrong assertion (that the figure eight knot and the trefoil have the same Conway polynomial - they don't). These are not important and won't lead you too far astray if you are paying attention.

Nicely presented and nicely bound, this book is a delight!