Introduction to knot theory/ R. H. Crowell

Prerequisites.- I * Knots and Knot Types.-
1. Definition of a knot.-
2. Tame versus wild knots.-
3. Knot projections.-
4. Isotopy type, amphicheiral and invertible knots.-
II *; The Fundamental Group.-
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.-
III * The Free Groups.-
1. The free group F[A].-
2. Reduced words.-
3. Free groups.-
IV * Presentation of Groups.-
1. Development of the presentation concept.-
2. Presentations and presentation types.-
3. The Tietze theorem.-
4. Word subgroups and the associated homomorphisms.-
5. Free abelian groups.-
V * Calculation of Fundamental Groups.-
1. Retractions and deformations.-
2. Homotopy type.-
3. The van Kampen theorem.-
VI * Presentation of a Knot Group.-
1. The over and under presentations.-
2. The over and under presentations, continued.-
3. The Wirtinger presentation.-
4. Examples of presentations.-
5. Existence of nontrivial knot types.-
VII * The Free Calculus and the Elementary Ideals.-
1. The group ring.-
2. The free calculus.-
3. The Alexander matrix.-
4. The elementary ideals.-
VIII * The Knot Polynomials.-
1. The abelianized knot group.-
2. The group ring of an infinite cyclic group.-
3. The knot polynomials.-
4. Knot types and knot polynomials.-
IX * Characteristic Properties of the Knot Polynomials.-
1. Operation of the trivialize.-
2. Conjugation.-
3. Dual presentations.-