Introduction to Differentiable Manifolds (Universitext)

From the reviews:

This volume is an introduction to differential manifolds which is intended for post-graduate or advanced undergraduate students. ... Basic concepts are presented, which are used in differential topology, differential geometry, and differential equations. Charts are used systematically ... . The book is well readable, and it is of interest not only for mathematicians, but also for theory-oriented researchers in applied sciences, who need an introduction to this important topic. (I. Troch, Internationale Mathematische Nachrichten, Issue 196, 2004)

The author recommends his text to `the first year graduate level or advanced undergraduate level' ... . his explanation is very precise, with rich formalism and with maximum generality ... . In summary, this is an ideal text for people who like a more general and abstract approach to the topic. (EMS, June, 2003)

The book offers a quick introduction to basic concepts which are used in differential topology, differential geometry and differential equations. ... The bibliography contains important new titles in studying differential geometry. A large index is also included. This is an interesting Universitext (for students - the first year graduate level or advanced undergraduate level), with important concepts concerning the general basic theory of differential manifolds. (Corina Mohorianu, Zentralblatt MATH, Vol. 1008, 2003)