  Starting from the (apparently) elementary problem of deciding how many
different topological spaces can be obtained by gluing together in pairs the
faces of an octahedron, we will describe the central role played by hyperbolic
geometry within three-dimensional topology. We will also point out the striking
difference with the two-dimensional case, and we will review some of the
results of the combinatorial and computational approach to three-manifolds
developed by different mathematicians over the last several years.

Geometric Topology