The theory of coverings allows to link properties between different manifolds whenever a special map exists between them. This permits the study of complicated manifolds from simpler ones. In this chapter, we explore unramified and ramified spaces which involve fundamental notions of covering spaces over manifolds. Roughly speaking, an unramified covering is a surjective map between manifolds which makes them locally homeomorphic. Fixing the base manifold, there is a beautiful relationship between all covering spaces and the fundamental group of the base manifold, similar to the Galois theory of field extensions. Allowing for special points at which the manifolds are not locally homeomorphic leads to ramified coverings, a much more flexible notion.