%0 Journal Article %T Waldhausen's Theorem %A Saul Schleimer %J Mathematics %D 2009 %I arXiv %R 10.2140/gtm.2007.12.299 %X This 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. %U http://arxiv.org/abs/0904.0182v1