Introduction to Smooth Manifolds

Preface * Smooth Manifolds * Smooth Maps * Tangent Vectors * Vector Fields * Vector Bundles * The Cotangent Bundle * Submersions, Immersions, and Embeddings * Submanifolds * Lie Groups Actions * Embedding and Approximation Theorems * Tensors * Differential Forms * Orientations * Integration on Manifolds * De Rham Cohomology * The de Rham Theorem * Integral Curves and Flows * Lie Derivatives * Integral Manifolds and Foliations * Lie Groups and Their Lie Algebras * Appendix: Review of Prerequisites * References * Index