1.Manifolds. 2.Hypersurfaces of Rn. 3.Surfaces in R3. 4.Tensors and forms. 5.Connexions. 6.Riemannian manifolds and submanifolds. 7.Operators on forms and integration. 8.Gauss-Bonnet theory and rigidity. 9.Existence theory. 10.Topics in Riemannian geometry.