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Résumé: Lie algebras and their representations form an extremely rich and important field of mathematics. Geometric representation theory is a relatively new field which has attracted much attention. The general idea is to use geometric methods to construct classically algebraic objects, such as representations of Lie groups and Lie algebras. Geometric techniques have proven to be particularly well suited to establishing positivity and integrality results, as these are often easy consequences of the geometric nature of the objects involved. One is also often able to use the representation theory of objects such as (affine) Kac-Moody algebras to organize and better understand the homology of various interesting spaces appearing in the constructions, like Hilbert schemes, flag varieties, Steinberg varieties, affine Grassmannians, and quiver varieties. In addition to its obvious connections to representation theory, geometric representation theory has been found to be intimately related to combinatorics (crystals, quivers), cluster algebras, mathematical physics, and many other subjects.