The purpose of this monograph is to make available in English the elementary parts of classical algebraic number theory. An earlier version in mimeographed form was used at Cornell University in the spring term of 1947–48, and the present version has accordingly profited from the criticisms of several readers. I am particularly indebted to Miss Leila R. Raines for her painstaking assistance in the revision and preparation of the manuscript for publication.

Preface to Second Edition

This new edition follows closely the plan and style of the 1st edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems. The credit for this revision is almost entirely due to my associate, Harold G. Diamond.

We are grateful to many contributors for both corrections and problems: P. T. Bateman, B. C. Berndt, P. T. Montague, Ivan Niven, J. Steinig, and S. V. Ullom.