Chapter 1 Unique Factorization
Chapter 2 Applications of Unique Factorization
Chapter 3 Congruence
Chapter 4 The structure of U
Chapter 5 Quadratic Reciprocity
Chapter 6 Quadratic Gauss Sums
Chapter 7 Finite Fields
Chapter 8 Gauss and Jacobi Sums
Chapter 9 Cubic and biquadratic reciprocity
Chapter 10 Equation over finite fields
Chapter 11 The zeta function
Chapter 12 Algebraic number theory
Chapter 13 Quadatic and cyclotomic fields
Chapter 14 The stickelberger realton and the eisenstein reciprocity law
Chapter 15 Bernoulli numbers
Chapter 16 Dirichlet L-fictions
Chapter 17 Diophantine equation
Chapter 18 Elliptic curves
Chapter 19 The modell-weil theorem
Chapter 20 New progress in arithmetic geometry

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 development is stressed throughout, along with wide-ranging coverage of significant results with comparatively 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 Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves. ---Summary provided by publisher