This international symposium aims at bringing together leading experts in the field of number theory, algebraic and arithmetic algebraic geometry. The objective is to outlay a state-of-the-art picture of this very active branch of mathematics, and to enhance research collaboration on outstanding problems. The symposium consists of the following four workshops: the André-Oort Conjecture, Serre's Modularity Conjecture, Periods, Hyperbolic and Arithmetic Geometry.