This volume covers the proceedings of the International Colloquium organised by the Tata Institute of Fundamental Research in January 2008, one of a series of Colloquia going back to 1956. It covers a wide spectrum of mathematics, ranging over algebraic geometry, topology, automorphic forms and number theory.

Algebraic cycles form the basis for the construction of motives, and conjectures about motives depend ultimately on important problems related to algebraic cycles, like the Hodge and the Tata Conjectures. Shimura Varieties provide interesting, nontrivial instances of these fundamental problems. On the other hand, the Motives of Shimura Varieties are of great interest in automorphic forms and number theory.

This book contains refereed articles by leading experts in these fields, containing original results, as well as expository material, on these areas.