This self-contained treatment is suitable for advanced undergraduate and graduate students and may be used either after or concurrently with courses in general topology and algebra. It surveys several algebraic invariants: the fundamental group, singular and Cech homology groups, and a variety of cohomology groups. 1970 edition. Reprint of the W. A. Benjamin, Inc., New York, 1970 edition.
Here's a sample of other books in this Dover category
Introduction to Topology: Second Edition by Theodore W. Gamelin, Robert Everist Greene This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
Topology: An Introduction to the Point-Set and Algebraic Areas by Donald W. Kahn Comprehensive coverage of elementary general topology as well as algebraic topology, specifically 2-manifolds, covering spaces and fundamental groups. Problems, with selected solutions. Bibliography. 1975 edition.
Basic Algebra I: Second Edition by Nathan Jacobson A classic text and standard reference for a generation, this volume covers all undergraduate algebra topics, including groups, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. 1985 edition.