This account of Algebraic Number Theory is written primarily for beginning graduate students in pure mathematics, and encompasses everything that most such students are likely to need; others who need the material will also find it accessible. It assumes no prior knowledge of the subject, but a firm basis in the theory of field extensions at an undergraduate level is required, and an appendix covers other prerequisites. The book covers the two basic methods of approaching Algebraic Number Theory, using ideals and valuations, and includes material on the most usual kinds of algebraic number field, the functional equation of the zeta function and a substantial digression on the classical approach to Fermat's Last Theorem, as well as a comprehensive account of class field theory. Many exercises and an annotated reading list are also included.

### Contents

Preface; 1. Numbers and ideals; 2. Valuations; 3. Special fields; 4. Analytic methods; 5. Class field theory; Appendix; Exercises; Suggested further reading.

### Prize Winner

2002 Choice Outstanding Academic Title Award Winner

### Reviews

"This little book would be a good place to find out what the subject is all about...this is not an easy book to read, but it is one that will reward the reader's efforts." MAA Online

"I like short concise yet rigorous books such as this one. You can learn a lot of number theory in 140 pages, and then you have a nice concise reference book when you forget what you learned!" The Bulletin of Mathematical Books