This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great ex

This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie

The present volume supersedes my Introduction to Differentiable Manifolds written a few years back. I have expanded the book considerably, including things like

Differential geometry began as the study of curves and surfaces using the methods of calculus. This book offers a graduate-level introduction to the tools and s

This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic