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What's good book for learning Algebraic Number Theory with minimum prerequisites? Assume that the reader has done an basic abstract algebra course.

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@jspecter I was about to recommend the very same! With a few more words your comment would make a good answer. –  Dylan Moreland Sep 20 '11 at 15:07
It would help if you revealed more about your goals. For example, do you plan to go on to do research in number theory or, is your aim to obtain a solid background for applications such as cryptography? –  Bill Dubuque Sep 20 '11 at 17:55
Research in Number theory. Actually, I'm interested in the Langlands program. –  Mohan Sep 21 '11 at 8:18

5 Answers 5

I'm a big fan of Murty and Esmonde's "Problems in algebraic number theory", which develops the basic theory through a series of problems (with the answers in the back). Another nice sources in Milne's notes on algebraic number theory, available on his website here.

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Milne's notes have answers at the end as well. –  Dylan Moreland Sep 20 '11 at 15:08

I would recommend Ireland and Rosen's text Classical Introduction to Modern Number Theory. The prerequisites for the first 10 or so chapters are minimal (first semester undergraduate algebra course).

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I would recommend Stewart and Tall's Algebraic Number Theory and Fermat's Last Theorem for an introduction with minimal prerequisites. For example you don't need to know any module theory at all and all that is needed is a basic abstract algebra course (assuming it covers some ring and field theory). But again the first chapter gives a quick review of the basic material from abstract algebra that is used later on.

I have used this book when I took an introductory course in Algebraic Number Theory and the experience was really good. The book has many examples and the pace is not too fast.

Most other books I have seen rely more heavily on module theory to make the exposition more general but since probably you don't have that background yet then I guess that this book may very well suit you perfectly.

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I like Algebraic Number Theory, Second Edition by Richard A. Mollin. It is simple and best book to self study.

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