We show that any 2- or 3-dimensional manifold is a branched covering of the sphere branched over a universal branching set. Using the associated unbranched covering, we show that there is a one-to-one correspondence between these branched coverings and pairs of permutations. In particular, this gives a means of studying manifolds. The goal of this work is to determine how much information about the manifold is readily accessible from the permutations.