Given a topological space X and a Lie group G, topologists investigated the class of principal G-bundles arising from homomorphisms from the fundamental group of X to G. The analogous construction works in Algebraic Geometry and plays an important role in Galois Cohomology (that is, when the base is a field) and also in the case where X is an abelian variety (or a torus). After presenting the above topics, we will focus on the case of the localization of a local henselian ring A with respect to a strict normal crossing divisor D which relates to the theory of Abhyankar covers. -- This seminar is part of the activities of the Project PRIN 2022S8SSW2 funded by the European Union – Next Generation EU.