An understanding of topology is fundamental to the grasp of most branches of mathematical analysis and geometry. This wide-ranging treatment opens with basic concepts of set theory and topological spaces; it concludes with the rudiments of functional analysis. Its remarkable depth contributes to its versatility as a classroom text, a guide for independent study, and a reference. Suitable for advanced undergraduates and graduate students, this volume can serve as a text for a complete course in topology. Its comprehensive scope and coherent presentation make it equally valuable as a self-contained guide for those wishing to study at their own pace. Additional enrichment materials and advanced topic coverage—including extensive material on differentiable manifolds, abstract harmonic analysis, and fixed point theorems—constitute an excellent reference for mathematics teachers, students, and professionals.