Reverse mathematics is a new field that seeks to find the axioms needed to prove given theorems. In *Reverse Mathematics*, John Stillwell offers a historical and representative view, emphasizing basic analysis and giving a novel approach to logic. By using a minimum of mathematical logic in a well-motivated way, *Reverse Mathematics* will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.

**John Stillwell** is professor of mathematics at the University of San Francisco and an affiliate of the School of Mathematical Sciences at Monash University, Australia. His many books include *Mathematics and Its History* and *Elements of Mathematics *(Princeton).

"If you are not familiar with this relatively new research about the foundations and and minimal assumptions needed to develop the massive mathematical structure, this provides a good informal guideline."**—Adhemar Bultheel, ***European Mathematical Society*

"John Stillwell’s book gives a clear and engaging introduction to an intriguing area of mathematics: reverse mathematics."**—Martyn Prigmore, ***Mathematics Today*

"The field has been due for a general treatment accessible to undergraduates and to mathematicians in other areas. . . . With *Reverse Mathematics*, John Stillwell provides exactly that kind of introduction."—Carl Mummert, *Notices of the American Mathematical Society*

"Stillwell carefully situates the field in the broader context of the history of mathematics and its foundations, and does a fine job of making the whole endeavor accessible to a general mathematical audience."—Jeremy Avigad, Carnegie Mellon University

"Filling an important niche, this book gives readers a good picture of the basics of reverse mathematics while suggesting several directions for further reading and study."—Denis Hirschfeldt, University of Chicago

"Stillwell's book is self-contained and includes much background material in analysis, mathematical logic, combinatorics, and computability. I heartily commend this very readable and accessible book."—Stephen Simpson, Vanderbilt University