An Introduction to Algebraic Topology (Dover Books on Mathematics)

This self-contained treatment of algebraic topology assumes only some knowledge of real numbers and real analysis. The first three chapters focus on the basics of point-set topology, offering background to students approaching the subject with no previous knowledge. Readers already familiar with point-set topology can proceed directly to Chapter 4, which examines the fundamental group as well as homology groups and continuous mapping, barycentric subdivision and excision, the homology sequence, and simplicial complexes.
Exercises form an integral part of the text; they include theorems that are as valuable as some of those whose proofs are given in full. Author Andrew H. Wallace, Professor Emeritus at the University of Pennsylvania, concludes the text with a guide to further reading.