Differentiable Manifolds

1 Differentiable manifolds and smooth maps 2 1.1 Coordinates on familiar spaces. Examples. . . . . . . . . . . . 2 1.2 Definition of a manifold. . . . . . . . . . . . . . . . . . . . . . 4 1.3 Smooth functions and smooth maps . . . . . . . . . . . . . . . 8 1.4 Constructions of manifolds. . . . . . . . . . . . . . . . . . . . 11 1.5 Appendix. The notion of a category . . . . . . . . . . . . . . . 16