  This is the authors doctoral thesis written at the Humboldt-University
Berlin. It contains material from the three separate papers: "On the Kodaira
dimension of the moduli space of nodal curves", "On quotients of
$\overline{\mathcal{M}}_{g,n}$ by certain subgroups of $S_n$" and "The moduli
space of hyperelliptic curves with marked points".
