An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised

Rating:
Summary: great introductory text
Review: My first course on manifolds was based on this book, and I believe that it is the best introduction to the subject (especially for beginners). I thoroughly enjoyed it! I should also recommend Conlon's 'Differentiable Manifolds' (2ed, Birkhauser), as it is the perfect follow-up to Boothby. --A

Rating:
Summary: great introductory text
Review: My first course on manifolds was based on this book, and I believe that it is the best introduction to the subject (especially for beginners). I thoroughly enjoyed it! I should also recommend Conlon's 'Differentiable Manifolds' (2ed, Birkhauser), as it is the perfect follow-up to Boothby. --A

Rating:
Summary: Very Nice Nontrivial Introduction
Review: This book is a careful treatment of the subjects in the title. It is an introduction, but it manages to cover quite a bit of ground with lots of examples to illustrate. One of it's distinguishing points is the way in which the concrete, coordinate based calculations are emphasized even while usually presenting the more abstract, coordinate free approach as well.

The book does a good job at stimulating those studying it to develop intuition. I found the book helpful when I was first studying the subject.