This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. 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.

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.

Preface.- 1 Introduction.- 2 Topological Spaces.- 3 New Spaces from Old.- 4 Connectedness and Compactness.- 5 Cell Complexes.- 6 Compact Surfaces.- 7 Homotopy and the Fundamental Group.- 8 The Circle.- 9 Some Group Theory.- 10 The Seifert-Van Kampen Theorem.- 11 Covering Maps.- 12 Group Actions and Covering Maps.- 13 Homology.- Appendix A: Review of Set Theory.- Appendix B: Review of Metric Spaces.- Appendix C: Review of Group Theory.- References.- Notation Index.- Subject Index.