This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in advanced undergraduate or first-year graduate courses. Reviews Indeed, the book is affordable (in fact, the most affordable of all references on the subject), but also a high quality work and a complete introduction to the rich theory of the arithmetic of elliptic curves, with numerous examples and exercises for the reader, many interesting remarks and an updated bibliography. Mathematical Reviews, Álvaro Lozano-Robledo J. S. Milne's lecture notes on elliptic curves are already well-known ... The book under review is a rewritten version of just these famous lecture notes from 1996, which appear here as a compact and inexpensive paperback that is now available worldwide. Zentralblatt MATH, Werner Kleinert