Topology is a difficult to define branch of advanced mathematics that has more bearing on math courses today than it did when outer space was out-of-bound. ""In one sense it is the study of continuity: beginning with space, or shapes, it generalizes, and then by analogy leads into other kinds of continuity -- and space as we generally understand it -- is left far behind."" Although ""really high-bouncing topologists not only avoid anything like pictures of these things..."" the book is generously illustrated with explanatory figures to support the introductory text. The author, who must take the student from the realm of the tangible and measurable to that of the abstract, keeps a light heart and his tongue in his cheek throughout the book. He keeps his explanations and examples as clearly worded as possible. While the book is not difficult to read, the subject is not an easy one to follow. The audience will be limited, but for the elite of the math class, this book is the one of its kind.