Intersection theory on moduli spaces of curves I

Modern applications of algebraic curves often deal with families of curves rather than individual ones. Therefore, the most universal such families, namely, moduli spaces of curves, became the central object of study during the last decades. In spite of efforts of numerous groups all over the world, the results obtained by now are far from being final. The most spectacular results concern intersection theory of characteristic classes on Deligne-Mumford compactifications of the moduli spaces in question.
I am planning to describe ways to construct moduli spaces and their compactifications, as well as approaches to study intersections of characteristic classes. No preliminary knowledge is required.