Recent results on the topology of three-manifolds

We present several results on the classification of the topological and geometrical structures of closed 3-manifolds. In particular, we describe many important families of hyperbolic 3-manifolds and obtain combinatorial representations of them as branched coverings of the 3-sphere and by means of Dehn surgeries along knots and links. Finally, we determine the isometry groups, the volumes and the main algebraic invariants of the considered manifolds.