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.

Table of Contents

Chapter 1 Introduction

Chapter 2 Continuity

Chapter 3 Compactness and connectedness

Chapter 4 Identification spaces

Chapter 5 The fundamental group

Chapter 6 Triangulations

Chapter 7 Surfaces

Chapter 8 Simplicial homology

Chapter 9 Degree and LeJschetz number

Chapter 10 Knots and covering spaces