Preface. - 1 Smooth Manifolds. - 2 Smooth Maps. - 3 Tangent Vectors. - 4 Submersions Immersions and Embeddings. - 5 Submanifolds. - 6 Sard's Theorem. - 7 Lie Groups. - 8 Vector Fields. - 9 Integral Curves and Flows. - 10 Vector Bundles. - 11 The Cotangent Bundle. - 12 Tensors. - 13 Riemannian Metrics. - 14 Differential Forms. - 15 Orientations. - 16 Integration on Manifolds. -17 De Rham Cohomology. -18 The de Rham Theorem. - 19Distributions and Foliations. -20 The Exponential Map. -21 Quotient Manifolds. - 22 Symplectic Manifolds. - Appendix A: Review of Topology. - Appendix B: Review of Linear Algebra. - Appendix C: Review of Calculus. - Appendix D: Review of Differential Equations. - References. - Notation Index. - Subject Index. Language: English