Introduction to Topological Manifolds

by John M. Lee

The preface and Chapter 1 are available for downloading in PDF format.  You need the Adobe Acrobat Reader to view them.
Preface
  1. Introduction
  2. Topological Spaces
  3. New Spaces From Old
  4. Connectedness and Compactness
  5. Simplicial Complexes
  6. Curves and Surfaces
  7. Homotopy and the Fundamental Group
  8. Circles and Spheres
  9. Some Group Theory
  10. The Seifert-Van Kampen Theorem
  11. Covering Spaces
  12. Classification of Coverings
  13. Homology
Appendix: Review of Prerequisites

References

Index

Introduction to Topological Manifolds