Lecture 1. Moduli spaces of pairs and of bundles: We shall describe the moduli spaces of pairs, its relationship with the moduli of bundles, with emphasis on the role of the stability parameter and the birational transformations which happen when varying it, which are called flips.

Lecture 2. Torelli theorem: We use an inductive argument on the rank involving the moduli spaces of bundles and the moduli of pairs to get topological and geometrical properties like: irreducibility, Picard groups, or "Torelli theorems" which say that the moduli space determines the curve.

Lecture 3. Hodge structures: We study more specific properties of the algebraic structure of the moduli spaces, like the (mixed) Hodge structures.

Lecture 4. Hodge-Deligne polynomials: We give the computation of Hodge-Deligne polynomials of the moduli spaces of pairs for small rank. This gives in particular the Poincaré polynomials of the moduli spaces. An analogous procedure allows to determine the K-theory class of these spaces.