Ricci Flow On 3-Manifolds With Positive Ricci Curvature

R.S.Hamilton's paper "Three manifolds with positive curvature" started an innovative research method called "Ricci Flow" on the Geometric topics.In this paper he demon-strate that every compact 3-manifold with positive Ricci Curvature also admits a metric of constant positive curvature under the evolution equation and then it's homeomorphic to a 3 dimension sphere. The main techniques used in his paper are short time existence of an degenerative second order parabolic partial dif-ferential equation and Maximum Principle about the parabolic equation. In the proof for the existance of the equation Hamilton resort to Nash-Moser implicit functional theory,however,now DeTurck has given more direct method(DeTurck trick). My work in this paper is only explanations on Hamilton's paper, including detailed proof on lemma and theory in Hamilton's paper, and sometimes my own comprehension on cer-tain problems.