The first two of a series of seminars and lectures on Ricci Flow and its applications, lecture I at at 1330 and lecture II at 1450 on Mon February 19th. Abstract: This is an introductory two part lecture on the Poincare conjecture, Geometrization and Ricci flow intended for both mathematicians and physicists (assuming some familiarity with the basic notions of differential geometry). Part I: The Poincare conjecture and Thurston's Geometrization Conjecture. We will begin by describing the 3-dimensional Poincare conjecture, a pure topology problem about 3-manifolds. Motivated by analogies with the 2-dimensional case we will see how Thurston brought geometry into 3-dimensional topology, the goal being to describe Thurston's Geometrization Conjecture. To do this we will describe both a little more topology (the sphere and torus decompositions) and a little geometry (a discussion of the 8 different types of homogeneous 3-manifolds). We will then see how the Poincare conjecture follows straightforwardly from the Geometrization Conjecture. Part II: Ricci flow and applications to Geometrization. After a very brief reminder of basic notions of curvature in differential geometry, we introduce the Ricci flow and try to explain why it should be seen as a natural nonlinear heat-type equation which diffuses curvature around a manifold. We will discuss (without proof) some of the very basic analytic results for Ricci flow and discuss the simplest solutions to Ricci flow (e.g. Einstein metrics, Ricci solitons, product metrics). We will describe some of Hamilton's fundamental early work which showed that Ricci flow can be used to geometrize certain 3-manifolds, and discuss why for topological reasons we know that the Ricci flow must usually develop singularities in finite-time. We discuss the general framework in which to analyse singularities of the Ricci flow, the pre-Perelman progress in this theory and what obstructions Perelman needed to overcome to use Ricci-flow (with surgery) to prove the Geometrization Conjecture. (A discussion of Perelman's contributions will be left for another occasion).