A Guide to Topology is part of the MAA Guides series. As such, this book is intended to provide an overview of topology for graduate students preparing for qualifying exams. It emphasizes point-set topology, with an eye towards applications in analysis. The book is succinct, but provides many examples that clarify the definitions and the differences among topological spaces. There are relatively few proofs. Those provided illustrate how the definitions are typically used.
The book is ideal for its target audience, covering many concepts in a mere 85 pages. The author suggests the book could also serve as a reference work. It is indeed a pleasant book to read. However, most mathematicians will be familiar with some of the material, and can find satisfactory information about what they do not on Wikipedia.
John Curran is Assistant Professor of Mathematics, Eastern Michigan University, where he coordinates the actuarial science program.