Alaca S., Williams K. Introductory Algebraic Number Theory 2004

Textbook in PDF format

Algebraic number theory is a subject that came into being through the attempts of mathematicians to try to prove Fermat’s last theorem and that now has a wealth of applications to Diophantine equations, cryptography, factoring, primality testing, and public-key cryptosystems.
This book provides an introduction to the subject suitable for senior undergraduate and beginning graduate students in mathematics. The material is presented in a straightforward, clear, and elementary fashion, and the approach is hands on, with an explicit computational flavor. Prerequisites are kept to a minimum, and numerous examples illustrating the material occur throughout the text. References to suggested readings and to the biographies of mathematicians who have contributed to the development of algebraic number theory are given at the end of each chapter. There are more than 320 exercises, an extensive index, and helpful location guides to theorems and lemmas in the text