This volume presents the refereed proceedings of the 1st Algorithmic Number Theory Symposium, ANTS-I, held at Cornell University, New York, in May 1994. The 35 papers accepted for inclusion in this book address many issues of the algorithmic, computational and complexity-theoretic aspects of number theory. The book also contributes to foundational research in cryptology and coding. Of particular value is a collection entitled "Open Problems in Number Theoretic Complexity", which presents 36 central open problems and relates them to the literature by means of some 160 references.