Announced in this paper. Differential Geometry meets Geometric Surgery on three-manifolds; Perelman clarified and (perhaps) corrected. A COMPLETE PROOF OF THE POINCAR´E AND GEOMETRIZATION CONJECTURES – APPLICATION OF THE HAMILTON-PERELMAN THEORY OF THE RICCI FLOW HUAI-DONG CAO† AND XI-PING ZHU‡ Abstract. "In this paper, we give a complete proof of the Poincar´e and the geometrization conjectures. This work depends on the accumulative works of many geometric analysts in the past thirty years. This proof should be considered as the crowning achievement of the Hamilton-Perelman theory of Ricci flow. " The first sections give a clear history of the recent approaches to the Poincare Conjecture and Thurman's Geometric Conjecture, which are joined at the hip. The guy who I feel sorry for is Hamilton, who did fantastic things to lay almost all of the groundwork for the solution but, like Moses, was not able to enter the promised land.