In addition to an introduction to mathematical logic, set theory, and the various methods of proof, this textbook prepares students for future courses by providing a strong foundation in the fields of number theory, abstract algebra, and analysis. Also included are a wide variety of examples and exercises as well as a rich selection of unique projects that provide students with an opportunity to investigate a topic independently or as partof a collaborative effort.

New features of the Second Edition include the addition of formal statements of definitions at the end of each chapter; a new chapter featuring the Cantor-Schröder-Bernstein theorem with a spotlight on the continuum hypothesis; over 200 new problems; two new student projects; and more. An electronic solutions manual to selected problems is available online.

 From the reviews of the First Edition:

"The book.emphasizes Pòlya's four-part framework for problem solving (from his book How to Solve It).[it] contains more than enough material for a one-semester course, and is designed to give the instructor wide leeway in choosing topics to emphasize.This book has a rich selection of problems for the student to ponder, in addition to "exercises" that come with hints or complete solutions.I was charmed by this book and found it quite enticing."

- Marcia G. Fung for MAA Reviews

". A book worthy of serious consideration for courses whose goal is to prepare students for upper-division mathematics courses. Summing Up: Highly recommended."

- J. R. Burke, Gonzaga University for CHOICE Reviews