The most recent observations indicate that the Universe is isotropic, with a small spatial curvature, which can be either positive, negative or zero. As is well known, Einstein’s theory of gravitation restricts the spatially isotropic sections of space time to be locally S^3, H^3 or E^3, respectively. Thus, the topology of the Universe is only partly determined. On the other hand there are a few effects which occur for non trivial topology. In this talk, we will give a brief discussion of some of these, in particular of the Casimir effect which should have been important in the primordial stages of the Universe.