Introductory material on the moduli space of curves

As a point of entry, there is the introductory book by Harris and Morrison, [HM98]. Moving towards the research front, two excellent expository papers on this material are those by Vakil [Vak03] and Corti [Cor97]. Further details can be found in the survey papers of Faber and Looijenga [FL99] and Hain and Looijenga [HL97]. Those interested in the construction of the moduli space should see [Edi00], which contains an excellent introduction to both Deligne-Mumford stacks and geometric invariant theory, and also constructs the moduli stack and moduli space of curves.