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. - Appendix I. Differentiable Knots are Tame. - Appendix II. Categories and groupoids. - Appendix III. Proof of the van Kampen theorem. - Guide to the Literature. Language: English