Introduction to Topological Manifolds
Second Edition, © 2011
by John M. Lee

From the back cover:

This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition.

Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.

This text is designed to be used for an introductory graduate course on the geometry and topology of manifolds. It should be accessible to any student who has completed a solid undergraduate degree in mathematics. The author’s book Introduction to Smooth Manifolds is meant to act as a sequel to this book.

About problems with print quality:

Many people have reported receiving copies of Springer books, especially from Amazon, that suffer from extremely poor print quality (bindings that quickly break, thin paper, and low-resolution printing, for example). This seems to be less likely to happen if you purchase directly from Springer, but even then it's not unheard of. Springer has told me they will replace any book with substandard print quality regardless of where you purchased it. Contact sales-ny@springernature.com for information.