In addition to the ones already mentioned:

J. Harer's lecture notes on the cohomology of moduli spaces (doesn't have all the proofs, but describes the main ideas related to the cell decomposition of the moduli spaces; Springer LNM something, I believe; unfortunately I'm away for the holidays and can't access Mathscinet to find a precise reference).

K. Strebel, Quadratic differentials (careful exposition of the complex analytic results used to construct the cell decomposition mentioned above; not much about moduli spaces or Teichm"uller theory though; Springer Erbebnisse).

L. Ahlfors, Lectures on quasi-conformal mappings (construction of Teichmuller spaces).

L. Ahlfors' and L. Bers's papers in Analytic functions, Princeton, 1960.