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 Calculations Involving the Classical Groups.- II Elements of K-Theory.- 8 Stability Properties of Vector Bundles.- 9 Relative K-Theory.- 10 Bott Periodicity in the Complex Case.- 11 Clifford Algebras.- 12 The Adams Operations and Representations.- 13 Representation Rings of Classical Groups.- 14 The Hopf Invariant.- 15 Vector Fields on the Sphere and Stable Homotopy.- III Characteristic Classes.- 16 Chern Classes and Stiefel-Whitney Classes.- 17 Differentiable Manifolds.- 18 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.
