Number Fields by Daniel A. Marcus

Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that highlights key arguments. There are several hundred exercises, providing a wealth of both computational and theoretical practice, as well as appendices summarizing the necessary background in algebra.

Now in a newly typeset edition including a foreword by Barry Mazur, this highly regarded textbook will continue to provide lecturers and their students with an invaluable resource and a compelling gateway to a beautiful subject.

From the reviews:

“A thoroughly delightful introduction to algebraic number theory” – Ezra Brown in the Mathematical Reviews

“An excellent basis for an introductory graduate course in algebraic number theory” – Harold Edwards in the Bulletin of the American Mathematical Society