This book is an outcome of the Millennial Conference on Number Theory held in 2000 at the University of Illinois at Urbana-Champaign. It reviews some of the major number theory achievements of this century and charts some of the directions in which the subject will be heading during the new century. "The conference was one of the most important international meetings devoted to number theory . . . . Consequently the interested reader finds here not only surveys on the most important contributions to number theory and its applications, but also surveys on methods and techniques used in this important branch of mathematics." -EMS Newsletter, December 2004