<P>This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, July 2006. The book presents 37 revised full papers together with 4
invited papers selected for inclusion. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves
over finite fields and applications, and discrete logarithms.</P>