This volume derives from the second Iberoamerican Congress on Geometry, held in 2001 in Mexico at the Centro de Investigacion en Matematicas AC, an internationally recognized programme of research in pure mathematics. The conference topics were chosen with an eye toward the presentation of new methods, recent results and the creation of more interconnections between the different research groups working in complex manifolds and hyperbolic geometry. This volume reflects both the unity and the diversity of these subjects. Researchers around the globe have been working on problems concerning...