  We introduce the moduli space of marked, complete, Nielsen-convex hyperbolic
structures on a surface of negative, but not necessarily finite, Euler
characteristic. The emphasis is on infinite type surfaces, the aim being to
study mapping class groups of infinite type surfaces via their action on this
marked moduli space. We define a topology on the marked moduli space and prove
that it reduces to the usual Teichm\"uller space for finite type surfaces. We
also prove that the action of the mapping class group on this marked moduli
space is continuous.
