2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70317A three-manifold equipped with a Heegaard diagram can be used to set up a Floer homology theory whose differential counts pseudo-holomorphic disks in the $g$-fold symmetric product of the Heegaard surface. This leads to a topological invariant for three-manifolds, Heegaard Floer homology, which is functorial under cobordisms. In this survey article, we sketch this construction and describe some of its topological applications.41 pages, 10 figuresGeometric TopologySymplectic Geometry57R58; 53D40; 57M27text