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The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
Colin C. Adams, Williams College, Williamstown, MA

2004; 307 pp; softcover
ISBN-10: 0-8218-3678-1
ISBN-13: 978-0-8218-3678-1
List Price: US$32
Member Price: US$25.60
Order Code: KNOT
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Knots are familiar objects. We use them to moor our boats, to wrap our packages, to tie our shoes. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. The Knot Book is an introduction to this rich theory, starting with our familiar understanding of knots and a bit of college algebra and finishing with exciting topics of current research.

The Knot Book is also about the excitement of doing mathematics. Colin Adams engages the reader with fascinating examples, superb figures, and thought-provoking ideas. He also presents the remarkable applications of knot theory to modern chemistry, biology, and physics.

This is a compelling book that will comfortably escort you into the marvelous world of knot theory. Whether you are a mathematics student, someone working in a related field, or an amateur mathematician, you will find much of interest in The Knot Book.

Colin Adams received the Mathematical Association of America (MAA) Award for Distinguished Teaching and has been an MAA Polya Lecturer and a Sigma Xi Distinguished Lecturer.

Other key books of interest available from the AMS are Knots and Links and The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes.

Request an examination or desk copy.


Undergraduates, graduate students, and research mathematicians interested in topology and knot theory.


From reviews of the first edition:

"Amazingly understandable ... After reading it twice, I still pick it up and scan it ... this book belongs in every mathematical library."

-- Charles Ashbacher, Book Reviews Editor, Journal of Recreational Mathematics

"Throughout the book there are lots of exercises of various degrees of difficulty. Many 'unsolved questions' provide opportunity for further research. I liked reading this book. ... well written, enjoyable to read, and very accessible."

-- Zentralblatt MATH

"I thought the book was very well suited for an undergraduate knot theory/ topology course. The exposition was very clear."

-- Jennifer Taback, Bowdoin College

Table of Contents

  • Introduction
  • Tabulating knots
  • Invariants of knots
  • Surfaces and knots
  • Types of knots
  • Polynomials
  • Biology, chemistry, and physics
  • Knots, links, and graphs
  • Topology
  • Higher dimensional knotting
  • Knot jokes and pastimes
  • Appendix
  • Suggested readings and references
  • Index
  • Corrections to the 2004 AMS printing
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