This book is based on notes I created for a one-semester undergraduate course on Algebraic Number Theory, which I taught at Harvard during Spring 2004. The primary sources for the course were chapter 1 of Swinnerton-Dyer's book A Brief Guide to Algebraic Number Theory [SD01] and chapter 2 of Cassels's article Global Fields [Cas67]. I wrote these notes by following closely the above two chapters; in some cases I added substantial text and examples. For example, chapter 1 of [SD01] is 30 pages, whereas my rewrite of it occupies over 100 pages. In contrast, I follow [Cas67] more closely. I have no intent whatever to plagiarize. I acknowledge as such those chapters in this book which are simply a close rewrite of [Cas67]. My goal is to take the useful classical article ([Cas67]) and make it more accessible to students by modernizing the notation, and adding additional explanations and examples.

I have no intent to publish this book with a traditional publisher, so it will remain freely available indefinitely. If you have comments, corrections, suggestions for additions, etc., please send them to me!


Copyright: William Stein, 2004.

License: FREE! More precisely, this book my be freely redistributed, copied, or even sold without requiring you to obtain written permission from me. You may even extend or change this book, but this preface page must remain in any derived work, and any derived work must also remain free, including the LATEX source files. In particular, I have no interest in making any money from this book.

Please send me any typos or corrections: [email protected].

Acknowledgement: This book closely builds on Swinnerton-Dyer's book [SD01] and Cassels's article [Cas67]. Many of the students of Math 129 at Harvard during Spring 2004 made helpful comments: Jennifer Balakrishnan, Peter Behrooz, Jonathan Bloom, David Escott Jayce Getz, Michael Hamburg, Deniz Kural, Danielle li, Andrew Ostergaard Gregory Price, Grant Schoenebeck, Jennifer Sinnott, Stephen Walker, Daniel Weissman, and Inna Zakharevich. Also the course assistant Matt Bainbridge made many helpful comments.

William Stein 2004-05-06