Knot Theory (Carus Mathematical Monographs)

Rating:
Summary: Excellent!
Review: Livingston does a good job on basic knot theory in this text. While Adams seems to jump around a bit in his book, Livingston keeps a nice flow to his work. The proofs require another text and a good background in algebra to understand, but the problems are wonderful for a deeper understanding of the material.

Rating:
Summary: A very thorough volume for the serious student
Review: Livingston's book is very concise and dense. It contains a lot of information, but is not the kind of book you could sit down and read through from cover to cover. It is excellent as a reference, a sort-of knot theory encyclopedia.

Rating:
Summary: A very thorough volume for the serious student
Review: Livingston's book is very concise and dense. It contains a lot of information, but is not the kind of book you could sit down and read through from cover to cover. It is excellent as a reference, a sort-of knot theory encyclopedia.

Rating:
Summary: Good for an introduction
Review: This book is an excellent introduction to knot theory for the serious, motivated undergraduate students, beginning graduate students,mathematicains in other disciplines, or mathematically oriented scientists who want to learn some knot theory.

Prequisites are a bare minimum: some linear algebra and a course in modern algebra should suffice, though a first geometrically oriented topology course (e. g., a course out of Armstrong, or Guillemin/Pollack) would be helpful.

Many different aspects of knot theory are touched on, including some of the polynomial invariants, knot groups, Alexander polynomial and related abelian invariants, as well as some of the more geometric invariants.

This book would serve as a nice complement to C. Adams "Knot Book" in that Livingston covers fewer topics, but goes into more mathematical detail. Livingston also includes many excellent exercises. Were an undergraduate to request that I do a reading course in knot theory with him/her, this would be one of the two books I'd use (Adam's book would be the other).

This book is intentionally written at a more elementary level than, say Kaufmann (On Knots), Rolfsen (Knots and Links), Lickorish (Introduction to Knot Theory) or Burde-Zieshcang (Knots), and would be a good "stepping stone" to these classics.