Bridging the gap between elementary number theory and the systematic study of advanced topics, A CLASSICAL INTRODUCTION TO MODERN NUMBER THEORY is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical developement is stressed throughout, along with wide-ranging coverage of significant results with comparitively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.