This text suitable for postgraduate students in mathematics offers a clear, comprehensive presen- tation of the fundamentals of topology. It can also be effectively used at the senior undergraduate level for a basic introduction to the core topics of topology. The book's broad coverage of topics and flexible organization allows instructors to follow their own preferences in the matter of course emphasis. The second edition is divided into two parts?general topology and algebraic topology. Table of Contents Preface. A Note to the Reader. Part I: GENERAL TOPOLOGY?Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and Paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. Part II: ALGEBRAIC TOPOLOGY? The Fundamental Group. Separation Theorems in the Plane. The Seifert-van Kampen Theorem. Classifi- cation of Surfaces. Classification of Covering Spaces. Applications to Group Theory. Bibliography. Index.