The concept of a group is central to essentially all of modern mathematics. In number theory and geometry where groups take central stage in various shapes such as symmetry groups, Galois groups, fundamental groups, reflection groups and permutation groups, the conceptual unification that it provides is most strikingly illustrated. In this school, we present groups and the natural objects they act on in a variety of arithmetic and geometric contexts. Special emphasis will be given to concrete examples, and practical and computational aspects of groups and their actions will be stressed. The topics to be treated include finite fields, coding theory covering spaces, representation theory, modular forms and Galois theory. All courses will be introductory courses.

Each course will consist of 6 lecture hours and 3 hours of training session devoted to solving exercises and to compttter assisted computations.