This wonderful book is an excellent introduction to elliptic curves over the rational numbers. It is self-contained and easily accessible, but still takes the reader quite far, thus giving an undergraduate reader some exciting glimpes of deeper mathematics. This book is ideally suited as a text book for an undergraduate course (I have myself enjoyed it as a course), but is written in a lively style that also makes it fun to read on one's own. It covers such topics as the Nagell-Lutz Theorem, Mordell's Theorem over rational numbers, elliptic curves over finite fields and reduction modulo p, Thue's Theorem and diophantine approximation, and even an introduction to complex multiplication. An appendix provides the reader with a basic background on projective geometry. This book is a must for any student wanting to see beyond the ordinary coursework, and at the same time provides a natural stepping stone to a more advanced treatment of the subject, such as "The Arithmetic of Elliptic Curves", also by Silverman, which has become pretty much the standard text on the subject.