2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73823A survey of tilings in the plane for a general audience.21 pages, 50 figures. Based on a Clay Public Lecture by the second author at the IAS/Park City Mathematics Institute in July, 2004. This new version includes major changes and corrections to Section 9Combinatorics52C20; 05B45text