The contents of this volume range from expository papers on several aspects of number theory, intended for general readers (Steinhaus property of planar regions; experiments with computers; Diophantine approximation; number field sieve), to a collection of research papers for specialists, which are at prestigious journal level. Thus the book leads the reader in many ways not only to the state of the art of number theory but also to its rich garden. Audience: Researchers and graduate students interested in recent developments in number theory.