Would anyone be able to recommend text books that give an introduction to Geometric Representation Theory and survey papers that give an outline of the work that has been done in the field? I'm looking for references that would be suitable as a follow up to James Humphrey's "Linear Algebraic Groups" and a first year graduate Algebraic Geometry course. I'd also prefer the texts to be in English but if it's necessary, I could also read references in French.

I would encourage you to consider "Representation Theory and Complex Geometry" by Chriss and Ginzburg. In particular, I think you might enjoy the realization of irreducible representations of the Weyl group of a complex semisimple group $G$ on the BorelMoore homology of the fibres of the Springer resolution of the nilpotent cone. For me, this has always been one of the motivating examples in geometric representation theory. 


Additionally to Peter Crooks answer I would recommend to study the book of Hotta and others : DModules, Perverse Sheaves, and Representation Theory Here you can learn about derived categories and perverse sheaves/dmodules (which are essential tools to study geometric representation theory) and how they are connected to representation theory. From here on it is not far to understand the geometry involved in the context of KazhdanLusztig theory, Koszul Duality (in the sense of Beillinson, Ginzburg and Soergel), the Geometric Satake equivalence (MirkovicVilonen). 


I am currently reading though the two books already mentioned (Representation Theory and Complex Geometry by Chriss and Ginzburg and DModules, Perverse Sheaves, and Representation Theory by Hotta et al) and I definitely recommend them. Two other references that I have found helpful are:


