  These are the lecture notes for my course at the 2011 Park City Mathematics
Graduate Summer School. The first two lectures covered the basics of the
Torelli group and the Johnson homomorphism, and the third and fourth lectures
discussed the second cohomology group of the level p congruence subgroup of the
mapping class group, following my papers "The second rational homology group of
the moduli space of curves with level structures" and "The Picard group of the
moduli space of curves with level structures".
