Foundations of differentiable manifolds and Lie groups / Franck W. Warner

Chapter 1, Manifolds; 2, Tensors and differential forms; 3, Lie Groups; 4, Integration on manifolds; 5, Sheaves, cohomology, and the de Rham theorem; 6, The Hodge theorem. These last two chapters assure this book a unique and extremely useful place among the "introductory books on manifold theory''.
Overall, the style is clear, clean, and formal, perhaps a bit thin on motivation, as is customary, except through examples and problems. The problems appearing after each chapter are elementary in the beginning, but after Chapter 2 the problems also contain significant major theorems. For example, the fundamental theorem on abelian Lie groups and the Peter-Weyl theorem are problems. Many problems are devoted to filling in necessary pieces of the text, e.g., a problem on the use of a partition of unity to prove the existence of a Riemannian metric is placed after Chapter 1, and problems on the star operator and the adjoint of left multiplication by a 1-form, both used in the Hodge theorem, are found after Chapter 2. (MathSciNet)

Bibliogr. p. 260-263. Index