In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for calculating them. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties will help students gain a rounded understanding of the subject.

1 Introduction.- 2 Continuity.- 3 Compactness and connectedness.- 4 Identification spaces.- 5 The fundamental group.- 6 Triangulations.- 7 Surfaces.- 8 Simplicial homology.- 9 Degree and Lefschetz number.- 10 Knots and covering spaces.- Appendix: Generators and relations.