This volume is dedicated to Professor John H. Coates, an outstanding contributor to number theory, both through his pioneering and fundamental mathematical works and through the magnificent mathematical school he has established. It contains 24 articles written by 38 authors on a wide range of topics in the cutting edge of research in number theory, algebraic geometry and analysis: zeta functions and $L$-functions, automorphic and modularity issues, Galois representations,arithmetic of elliptic curves, Iwasawa theory, noncommutative Iwasawa theory, and $p$-adic analysis. This volume will be of interest to researchers and students in these and neighboring fields. Information for our distributors: A publication of the Documenta Mathematica. The AMS distributes this series,beginning with volume 3, in the United States, Canada, and Mexico.