Number Fields 1: A Special Case of Fermat’s Conjecture 2: Number Fields and Number Rings 3: Prime Decomposition in Number Rings 4: Galois Theory Applied to Prime Decomposition 5: The Ideal Class Group and the Unit Group 6: The Distribution of Ideals in a Number Ring 7: The Dedekind Zeta Function and the Class Number Formula 8: The Distribution of Primes and an Introduction to Class Field Theory Appendix A: Commutative Rings and Ideals Appendix B: Galois Theory for Subfields of C Appendix C: Finite Fields and Rings Appendix D: Two Pages of Primes Further Reading Index of Theorems List of Symbols 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