Abstract
This thesis is devoted to the study of the Galois coverings of finite dimensional algebras. In particular, it investigates the existence of a universal cover and a fundamental group for finite dimensional connected and basic algebras over an algebraically closed field. For this purpose, we start from an already existing notion: the fundamental group associated with any presentation of such an algebra A by its ordinary quiver Q and admissible relations. We first compare the different presentations of A. The automorphisms of the path algebra kQ allow one to link two arbitrary presentations of A. Among these automorphisms, we distinguish the dilatations and the transvections: they generate the group of automorphisms of kQ, moreover, the fundemantal groups of two presentations of A linked by a transvection or a dilatation are related by a quotient relation. These properties allow us to exhibit a fundamental group for A when the ground field has characteristic zero and when Q has no double bypass. These considerations can be translated in terms of Galois coverings since any presentation gives rise to a Galois covering with group the fundamental group of the presentation. Hence, under the above hypotheses granting a fundamental group, A admits a universal cover. This last result is extended to the case where A is monomial, Q has no oriented cycles and no multiple arrows (but may have double bypasses) and where the ground field may have any characteristic.