Introduction to smooth manifolds 1. Smooth manifolds 2. Smooth maps 3. Tangent vectors 4. Submersions Immersions and embeddings 5. Submanifolds 6. Sards theorem 7. Lie groups 8. Vector fields 9. Integral curves and flows 10. Vector bundles 11. The contangent bundle 12. Tensors 13. Riemannian metrics 14. Differential forms 15. Orientations 16. Integration on manifolds 17. De Rham cohomology 18. The de Rham theorem 19. Distributions and foliations 20. The exponential map 21. Quotient manifolds 22. Symplectic manifolds Appendices