A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics)

Rating:
Summary: Covers many important areas
Review: I have devoted a good portion of my life to the study of mathematics in general, especially algebra and number theory. This book is an extraordinary reference to many areas of number theory and extremely approachable. The book can be studied on its own or as a companion piece to more specialized texts such as Marcus's Number Fields.

Rating:
Summary: Covers many important areas
Review: I have devoted a good portion of my life to the study of mathematics in general, especially algebra and number theory. This book is an extraordinary reference to many areas of number theory and extremely approachable. The book can be studied on its own or as a companion piece to more specialized texts such as Marcus's Number Fields.

Rating:
Summary: Simply Amazing
Review: I picked up this book as a junior in college and was simply stunned. The flow of ideas is so natural that there are times when you can even read the book like a novel. The exposition is clean, and the proofs are elegant.
However, keep in mind that this book IS a GTM. Hence, it requires pre-requisites by way of approximately a year of abstract algebra. As the author says in the preface, it's possible to read a the first 11 chapters without it. However, to appreciate the beauty of the theory, I would sincerely recommend algebra as pre-req.
The first 12 chapters can be considered 'elementary' (not easy, just fundamental). The others are specialized algebraic topics. For instance, the chapter on elliptic curves is useful to get a flavor of the subject. However, it includes very few proofs.

Rating:
Summary: A Modern Classic
Review: If ever there was a textbook of which one could say that it was a thing of beauty, this has to be it. The book is very clearly written, and it is readily accessible even to those without a deep understanding of algebra or analysis; despite this, it manages to touch upon a great deal of relatively sophisticated material, and in a way that makes clear the links between the problems of the past and those of the present. I'd imagine that the book would constitute an essential item of reference for anyone with more than a passing interest in number theory.