2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123682These are the notes for my lecture ``Resolution of Sigularities in Charcteristic 0" given at the AMS Summer Institute at Seattle. It gives a self contained proof of the strong Hironaka resolution theorem.Major changes in Section 3,6 and 10Algebraic Geometry14E15, 14J17 (primary) 32S45 (secondary)text