Symplectic reflection algebras

The symplectic reflection algebras have been introduced by Etingof and Ginzburg in 2000 in the paper: Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism. In this thesis, we present some of their basic properties and we compute an example in order to have a better understanding of the objects involved. Furthermore, we focus on a particular family of symplectic reflection algebras: the rational Cherednik algebras and we state a result of Etingof and Ginzburg on their centre at parameter t=0. To conclude, we introduce, following Bellamy, a quotient of the latter family of algebras at parameter t=0: the restricted rational Cherednik algebras and we recall from a work by Gordon some results on their representation theory. We conclude by computing an explicit example of the objects involved.