1 Preliminaries on Homotopy Theory. - I The General Theory of Fibre Bundles. - 2 Generalities on Bundles. - 3 Vector Bundles. - 4 General Fibre Bundles. - 5 Local Coordinate Description of Fibre Bundles. - 6 Change of Structure Group in Fibre Bundles. - 7 The Gauge Group of a Principal Bundle. - 8 Calculations Involving the Classical Groups. - II Elements of K-Theory. - 9 Stability Properties of Vector Bundles. - 10 Relative K-Theory. - 11 Bott Periodicity in the Complex Case. - 12 Clifford Algebras. - 13 The Adams Operations and Representations. - 14 Representation Rings of Classical Groups. - 15 The Hopf Invariant. - 16 Vector Fields on the Sphere. - III Characteristic Classes. - 17 Chern Classes and Stiefel-Whitney Classes. - 18 Differentiable Manifolds. - 19 Characteristic Classes and Connections. - 20 General Theory of Characteristic Classes. - Appendix 1 Dold's Theory of Local Properties of Bundles. - Appendix 2 On the Double Suspension. - 4. Single Suspension Sequences. - 7. Double Suspension Sequences. Language: English