This book was written as an introductory text for a one semester course and, as such, it is far from a comprehensive reference work. Its lack of completeness is now more apparent than ever since, like most branches of mathematics, knot theory has expanded enormously during the last fifteen years. The book could certainly be rewritten by including more material and also by introducing topics in a more elegant and up-to-date style. Accomplishing these objectives would be extremely worthwhile. However, a significant revision of the original work along these lines, as opposed to writing a new book, would probably be a mistake. As inspired by its senior author, the late Ralph H. Fox, this book achieves qualities of effectiveness, brevity, elementary character, and unity. These characteristics would be jeopardized, if not lost, in a major revision.

Prerequisites

Chapter Ⅰ Knots and Knot Types

1.Definition of a knot

2.Tame versus wild knots

3.Knot projections

4.Isotopy type， amphichelral and invertible knots

Chapter Ⅱ The Fundamentel Group

Introduction

1.Paths and loops

2.Classes of paths and loops

3.Change of basepoint

4.Induced homomorphisms of fundamental groups

5.Fundamental group of the circle

Chapter Ⅲ The Free Groups

Introduction

1.The free group

2.Reduced words

3.Free groups

Chapter Ⅵ Presentation of Groups

Introduction

1.Retractions and deformations

2.Homotopy type

3.The van Kampen theorem

Chapter Ⅵ Presentation of a Knot Guoup

Chapter Ⅶ The Free Calculus and the Elementary Ideals

Chapter Ⅷ The Knot Polynomials

Chapter Ⅸ Characteristic Proerties of the Knot Polynomials

Appendix Ⅰ.Differentable Knots are Tame

Appendix Ⅱ.Categories and groupoids

Appendix Ⅲ.Proof of the van Kampen theorm

Guide to the Literature

Biliography

Index