An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics)
Differentiable manifolds abd the differential and integral calculus of their associated structures, such as vectors, tensors, and differential forms are of great importance in many areas of mathematics and its applications.  Although basically and extension of advanced, or multivariable calculus, the leap from Euclidean space to manifolds can often be difficult.  It takes time and patience, and it is easy to become mirred in abstraction and generalization.In this text the author draws on his extensive experience in teaching this subject to minimize these difficulties.  The pace is relatively liesurely, inessential abstraction and generality are avoided, the essential ideas used from the prerequisite subjects are reviewed, and there is an abundance of accessible and carefully developed examples to illuminate new concepts and to motivate the reader by illustrating their power.  There are more than 400 exercises for the reader.This book has been in constant, successful use for more than 25 years and has helped several generations of students as well as working mathemeticians, physicists and engineers to gain a good working knowledge of manifolds and to appreciate their importance, beauty and extensive applications.