An introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more.
Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
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