Thorough, modern treatment, essentially from a homotopy theoretic viewpoint. Topics include homotopy and simplicial complexes, the fundamental group, homology theory, homotopy theory, homotopy groups and CW-Complexes, and other topics. Each chapter contains exercises and suggestions for further reading. 1980 corrected edition.
Here's a sample of other books in this Dover category
Topology by John G. Hocking, Gail S. Young Superb 1-year course in classical topology. Topological spaces and functions, point-set topology, much more. Examples and problems. Bibliography. Index.
Elementary Topology: Second Edition by Michael C. Gemignani Superb introduction to metric spaces, topologies, convergence, compactness, connectedness, homotopy theory, other essentials. Numerous exercises, plus section on paracompactness and complete regularity. References. Includes 107 illustrations.
Cohomology Operations and Applications in Homotopy Theory by Robert E. Mosher, Martin C. Tangora This treatment explores the single most important variety of cohomology operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications. 1968 edition.
A Treatise on Algebraic Plane Curves by Julian Lowell Coolidge A detailed introduction to the theory of algebraic plane curves and their relations to various fields of geometry and analysis, this text employs both algebraic and geometric methods. 1931 edition. 17 illustrations.
Point Set Topology by Steven A. Gaal Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 edition.