Introduced by B. Totaro, the weight filtration on the homology of real algebraic varieties, which is a real analog to P. Deligne's weight filtration for complex algebraic varieties, has been realized via a filtered chain complex by C. McCrory and A. Parusinski, especially through the study of the induced spectral sequence. Among the several pieces of information held by this weight spectral sequence, one can recover the virtual Betti numbers. In this thesis, we show the existence of an equivariant weight filtration on the equivariant homology of real algebraic varieties equipped with a finite group action. We realize it by a filtered complex and, via the construction of several spectral sequences, we make significative progress toward the extraction of additive invariants. During our study, we functorially define a weight complex with action and we show an analog of the Smith exact sequence, taking into account the Nash-constructible filtration, that follows from a result on the splitting of Nash manifolds with algebraic involutions. Through the construction of an invariant weight complex in the frame of algebraic involutions, we also recover G. Fichou's equivariant virtual Betti numbers. Finally, applying the relevant functors on T. Limoges' results on the products of real weight filtrations, we give results on the products of equivariant weight filtrations.
