2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225467This note is an exposition of Waldhausen's proof of Waldhausen's Theorem: the three-sphere has a single Heegaard splitting, up to isotopy, in every genus. As a necessary step we also give a sketch of the Reidemeister-Singer Theorem.This is the version published by Geometry & Topology Monographs on 3 December 2007Geometric Topology57M40, 57N10, 57Q15text