Lectures on the geometry of Manifolds

The object of this book is to introduce the reader to some of the most important techniques of modern global geometry. In writing it we had in mind the beginning graduate student willing to specialize in this very challenging field of mathematics. The necessary prerequisite is a good knowledge of the calculus with several variables, linear algebra and some elementary point-set topology.We tried to address several issues. 1. The Language; 2. The Problems; 3. The Methods; 4. The Answers.Historically, the problems came first, then came the methods and the language while the answers came last. Th