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What are the prerequisites for understanding the work of Perelman concerning the Poincaré conjecture?

I am referring to the last three papers here.

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    $\begingroup$ A simple Google search yields this: math.berkeley.edu/~lott/ricciflow/perelman.html . $\endgroup$
    – Marco Golla
    Commented Sep 14, 2015 at 6:48
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    $\begingroup$ The answers to this question are relevant. $\endgroup$
    – Thomas Richard
    Commented Sep 14, 2015 at 7:30
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    $\begingroup$ Terry Tao gave a course on Perelman's proof of the Poincare conjecture. The notes for this course were written up on his blog, under the tag 285G. The first of the lectures is here: terrytao.wordpress.com/2008/03/26/… $\endgroup$
    – Nick Gill
    Commented Sep 14, 2015 at 9:49
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    $\begingroup$ Try going through (that book itself has more prerequisites that you'll have to acquire on the way): Morgan, John; Tian, Gang Ricci flow and the Poincaré conjecture. Clay Mathematics Monographs, 3. American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2007. xlii+521 pp. $\endgroup$
    – Suvrit
    Commented Sep 14, 2015 at 13:21

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