2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108927We review the construction of Heegaard Floer homology for closed three-manifolds and also for knots and links in the three-sphere. We also discuss three applications of this invariant to knot theory: studying the Thurston norm of a link complement, the slice genus of a knot, and the unknotting number of a knot. We emphasize the application to the Thurston norm, and illustrate the theory in the case of the Conway link.To appear in the Proceedings for ICM-2006 MadridGeometric TopologySymplectic Geometry53D; 57Rtext