A great book is Albarello-Cornalba-Griffiths vol 2.
http://ncatlab.org/nlab/show/Mumford+class contains some good references.
arXiv:1109.2173 GIT Constructions of Log Canonical Models of M_g from arXiv Front: math.AG by Jarod Alper, Donghoon Hyeon The purpose of this article is to give an overview of the construction of moduli spaces of curves from the viewpoint of the log minimal model program for M_g by providing an update of recent developments and discussing future problems. This survey is distinguished from the recent articles of Fedorchuk-Smyth and Morrison in its focus on low degree Hilbert stability of curves.
nLab page on Moduli of curves