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: Doldโs theory of local properties of bundles -- appendix 2: On the double suspension -- 4. Single suspension sequences -- 7. Double suspension sequences

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