I gave three lectures in Marrakech in October 2011 about fully nonlinear parabolic equations. We then wrote with L. Silvestre complete proofs of all the results stated during these lectures (and others!).
Abstract. These notes contain a short exposition of selected results about parabolic equations: Schauder estimates for linear parabolic equations with Hölder coefficients, some existence, uniqueness and regularity results for viscosity solutions of fully nonlinear parabolic equations (including degenerate ones), the Harnack inequality for fully nonlinear uniformly parabolic equations.