1.Preliminaries on homotopy theory. 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. 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 rigns of classical groups. 14.The hoff invariant. 15.Vector fields on the sphere. 16.Characteristic classes, 17.Differentiable manifolds. 18.General theory of characteristic classes.