This is a draft of the lecture notes for my four lectures at the Park City Math Institute, Utah 2011. The lectures form a continuation of Nathalie Wahl’s lectures, and I refer to her lectures for context and motivation. My goal for the lectures will be to give a precise statement of the MadsenWeiss theorem and give (most of) a proof. The theorem was first proved by Madsen and Weiss in [4]. The ...