Higher Arithmetic: An Algorithmic Introduction to Number Theory (2008).: An extension of Edwards' work in Essays in Constructive Mathematics, this textbook covers the material of a typical undergraduate number theory course, but follows a constructivist viewpoint in focusing on algorithms for solving problems rather than allowing purely existential solutions. However, unlike much other work in algorithmic number theory, there is no analysis of how efficient these algorithms are in terms of their running time.
Divisor Theory (1990).:Algebraic divisors were introduced by Kronecker as an alternative to the theory of ideals. According to the citation for Edwards' Whiteman Prize, this book completes the work of Kronecker by providing "the sort of systematic and coherent exposition of divisor theory that Kronecker himself was never able to achieve."
Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (1977).: As the word "genetic" in the title implies, this book on Fermat's Last Theorem is organized in terms of the origins and historical development of the subject. It was written some years prior to Wiles' proof of the theorem, and covers research related to the theorem only up to the work of Ernst Kummer, who used p-adic numbers and ideal theory to prove the theorem for a large class of exponents, the regular primes.
↑Graduate Texts in Mathematics 50, Springer-Verlag, New York, 1977, ISBN 0-387-90230-9. Reprinted with corrections, 1996, ISBN 978-0-387-95002-0, . Russian translation by V. L. Kalinin and A. I. Skopin. Mir, Moscow, 1980, .
↑Review by Charles J. Parry (1981), Bulletin of the AMS4 (2): 218–222.