These notes are somewhat rough: they may contain some mistakes, so please use caution when reading them.
Some notes about Grassmannians. (PDF)
Some notes about the construction of the Hilbert scheme. Included are some notes on G.I.T. and the construction of the moduli spaces. (PDF)
Some notes containing a brief survey of the cohomology of the moduli space of curves and the Harer-Zagier formula for the orbifold Euler characteristic. I added a few words outlining other work of Harer on the stability of the cohomology of the moduli space of curves. (PDF)
Some notes describing the Picard group of the moduli space of curves. (PDF)
Some notes about the Kodaira dimension of the moduli space of curves. (PDF) You should also read Chapter 5 and 6F of Harris, J., and I. Morrison. Moduli of Curves. New York, NY: Springer-Verlag, 1998, p. 366. ISBN: 0387984380. (U.S.)
Some notes on the Kontsevich moduli space of genus zero stable maps. (PDF)