This book constitutes the refereed post-conference proceedings of the Second International Algorithmic Number Theory Symposium, ANTS-II, held in Talence, France in May 1996. The 35 revised full papers included in the book were selected from a variety of submissions. They cover a broad spectrum of topics and report state-of-the-art research results in computational number theory and complexity theory. Among the issues addressed are number fields computation, Abelian varieties, factoring algorithms, finite fields, elliptic curves, algorithm complexity, lattice theory, and coding.