Topology is an essential part of the mathematics of today. Not only is it important in its own right, but its ideas and viewpoints influence a wide variety of other mathematical fields. This book provides the reader with a modern account of the basic concepts of topological and uniform spaces, with an emphasis on the relation between the two. The material divides naturally into three sections; six chapters on topological theory, two chapters devoted to uniform theory and the final four chapters which draw on ideas from the first two sections. The text is designed for senior undergraduate and graduate students in pure mathematics who have a general understanding of sets, algebra and analysis. Based on the author's earlier book Topological and Uniform Spaces, the text has been thoroughly revised and expanded. Exercises, all with worked solutions, are provided to consolidate understanding of the concepts and techniques. A brief, informative essay on the history of the subject is also included. The Springer Undergraduate Mathematics Series (SUMS) is a new series of guides, written for undergraduates in the Mathematical Sciences. The books cover the basics of each topic via explanatory text, examples and problems. Students can read and check their understanding of the text against fully worked solutions.