This course is an introduction to the theory of differentiable manifolds. The topics covered include

- Charts, atlases, definition of a differentiable manifold

- Differentiable maps, tangent bundle

- Immersions, submersions, submanifolds

- Partitions of unity

- Vector fields, differential equations on a manifold

- Differential forms, exterior differential calculus

- Lie derivative, Lie-Cartan calculus

Other topics which may be covered:

- Approximation results

- Sard's lemma and applications

- Frobenius theorem

- Stokes' formula

- De Rham cohomology in maximal dimension, degree.

Espaces vectoriels topologiques. Topologies faibles. Dualité.

Théorie des distributions

Espaces de Sobolev

Opérateurs compacts et théorie de Fredholm