First Edition sold over 2500 copies in the Americas; New Edition contains three new chapters and two new appendices

From the reviews of the second edition:

Husemoeller's text was and is the great first introduction to the world of elliptic curves ... and a good guide to the current research literature as well. ... this second edition builds on the original in several ways. ... it has certainly gained a good deal of topicality, appeal, power of inspiration, and educational value for a wider public. No doubt, this text will maintain its role as both a useful primer and a passionate invitation to the evergreen theory of elliptic curves and their applications (Werner Kleinert, Zentralblatt MATH, Vol. 1040, 2004)

Introduction to Rational Points on Plane Curves * Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve * Plane Algebraic Curves * Factorial Rings and Elimination Theory * Elliptic Curves and Their Isomorphism * Families of Elliptic Curves and Geometric Properties of Torsion Points * Reduction mod p and Torsion Points * Proof of Mordell's Finite Generation Theorem * Galois Cohomology and Isomorphism Classification of Elliptic Curves over Arbitrary Fields * Descent and Galois Cohomology * Elliptic and Hypergeometric Functions * Theta Functions * Modular Functions * Endomorphisms of Elliptic Curves * Elliptic Curves over Finite Fields * Elliptic Curves over Local Fields * Elliptic Curves over Global Fields and l-adic Representations * L-Functions of an Elliptic Curve and Its Analytic Continuation * Remarks on the Birch and Swinnerton-Dyer Conjecture * Remarks on the Modular Curves Conjecture and Fermat's Last Theorem * Higher Dimensional Analogs of Elliptic Curves: Calabi-Yau Varieties * Families of Elliptic Curves * Appendix I: Calabi-Yau Manifolds and String Theory * Appendix II: Elliptic Curves in Algorithmic Number Theory * Appendix III: Guide to the Exercises * Bibliography * Index