Abstract: Moduli functors and moduli problems are ubiquitous in mathematics. They appear as soon as we want to understand what behaviour objects have when put in families. In this talk we will introduce the notion of semistable sheaf on a curve, and we will see that the moduli problem that parametrises families of semistable vector bundles of fixed rank and degree has a coarse moduli space, meaning that there is some scheme whose points parametrise equivalence classes of semistable vector bundles of rank r and degree n.