This book provides a tour through the main branches of the foundations of mathematics. It contains chapters covering elementary logic, basic set theory, recursion theory, Gödel's (and others') incompleteness theorems, model theory, independence results in set theory, nonstandard analysis, and constructive mathematics. In addition, this monograph discusses several topics not normally found in books of this type, such as fuzzy logic, nonmonotonic logic, and complexity theory.

The word "tour" in the title deserves some explanation. This word is meant to emphasize that this is not a textbook in the strict sense. To be sure, it has many of the features of a textbook, including exercises. But it is less structured, more free-flowing, than a standard text. It also lacks many of the details and proofs that one normally expects in a mathematics text. However, in almost all such cases there are references to more detailed treatments and the omitted proofs. Therefore, this book is actually quite suitable for use as a text at the university level (undergraduate or graduate), provided that the instructor is willing to provide supplementary material from time to time.

The most obvious advantage of this omission of detail is that this monograph is able to cover a lot more material than if it were a standard textbook of the same size. This de-emphasis on detail is also intended to help the reader concentrate on the big picture, the essential ideas of the subject, without getting bogged down in minutiae. This book could have been titled "A Survey of Mathematical Logic," but the author's choice of the word "tour" was deliberate. A survey sounds like a rather dry activity, carried out by technicians with instruments. Tours, on the other hand, are what people take on their vacations. They are intended to be fun. The goal of this book is similar: to provide an introduction to the foundations of mathematics that is substantial and stimulating, and at the same time a pleasure to read. It is designed so that any interested reader with some post-calculus experience in mathematics should be able to read it, enjoy it, and learn from it.