1.Smooth manifolds. 2.Smooth maps. 3.The tangent bundle. 4.The Cotangent bundle. 5.Submanifolds. 6.Embedding and approximation theorems. 7.Lie group actions. 8.Tensors. 9.Differential forms. 10.Integration on manifolds. 11.De Rham cohomology. 12.Integral curves and flows. 13.Lie derivatives. 14.Integral manifolds and foliations. 15.Lie algebras and Lie groups.