Weight filtration in the cohomology of Shimura varieties

Shimura varieties are algebraic varieties which are initially constructed, as complex analytic objects, as locally symmetric varieties with respect to a well-chosen semisimple algebraic group G. The first aim of the talk is to introduce these objects and to motivate the interest of the structures appearing in their cohomology. In a second part, we will explain some results which describe how the representation theory of the underlying group G controls the Hodge-theoretic weight filtration in the cohomology of Shimura varieties.