Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem.

Table of Contents

Chapter 1: Introduction

Chapter 2: The Basic Theory

Chapter 3: Torsion Points

Chapter 4: Elliptic Curves over Finite Fields

Chapter 5: The Discrete Logarithm Problem

Chapter 6: Elliptic Curve Cryptography

Chapter 7: Other Applications

Chapter 8: Elliptic Curves over Q

Chapter 9: Elliptic Curves over C

Chapter 10: Complex Multiplication

Chapter 11: Divisors

Chapter 12: lsogenies

Chapter 13: Hyperelliptic Curves

Chapter 14: Zeta Functions

Chapter 15: Fermat's Last Theorem

Appendix A: Number Theory

Appendix B: Groups

Appendix C: Fields

Appendix D: Computer Packages

About the Author

Lawrence Clinton Washington is an American mathematician at the University of Maryland who specializes in number theory.