Abstract: In mid-November 2002, Perelman posted a preprint on the ArXiv which introduced several new tools for controlling Hamilton's Ricci flow, and proved a number of deep results about the flow. In the concluding section he announced a solution to Thurston's Geometrization Conjecture, explaining (in a very brief sketch) how to combine the theorems in this paper to get a proof. The lecture will be an introduction to Perelman's paper. I will briefly discuss background on the Geometrization conjecture and Hamilton's Ricci flow approach, and then explain in broad terms what has been achieved in the paper, and what is still lacking. The last part of the lecture will be more technical, focusing on several key steps in his argument