A Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. Shimura varieties have a very rich geometric and arithmetic structure. For instance they are defined over a number field (the reflex field), they have line bundles provided with hermitian metrics that come from a representation of a maximal compact subgroup and sometimes they have models over a localization of a ring of integers coming from a modular interpretation.