This book is an ambitious but optimistic treatment of the subject of topology. Not only does it treat the standard basic material about point-set topology, it also gives an introduction to algebraic topology, a treatment of manifolds, a discussion of function spaces, some ideas of knot theory, a presentation of graph theory, and some ideas from dynamical systems. Even the exciting new topic of the Jones polynomial is covered.

After discussing the key ideas of topology, the author examines the more advanced topics of algebraic topology and manifold theory. He also explores meaningful applications in several areas, including the traveling salesman problem, digital imaging, mathematical economics, and dynamical systems. The appendices offer background material on logic, set theory, the properties of real numbers, the axiom of choice, and basic algebraic structures.

Topic coverage has been reduced in this edition, and exercise sets have been added at the end of each section. The book as a whole—and the first two chapters in particular— offer many examples. Solutions to odd-numbered exercises are included at the end.

Today’s students need a text that speaks to them in their own language, and at a pace with which they are comfortable. That is the goal of this edition. Taking a fresh and accessible approach to a venerable subject, this text provides excellent representations of topological ideas. It forms the foundation for further mathematical study in real analysis, abstract algebra, and beyond.