We will start with some general statements and ideas about Geometric structures and their holonomy representations. We will then go on to understand the action of mapping class group on the holonomies. We will then restrict to the case of $(\text{PSL}(2;\mathbb{R}),\mathbb{H}^2)$ representations and in particular, to the case of discrete and faithful representations, which is the Teichmüller space. We will prove the proper discontinuity of the action using Teichmüller metric and Wolpert's lemma.