On the Equation of an Origami of Genus two with two Cusps

An origami is a compact Riemann surface provided with a flat structure that comes from a covering map to a torus. Affine variations of the flat structure lead to a family of compact Riemann surfaces whose base is an algebraic curve in the moduli space, called Teichmueller curve. The main aim of this thesis is to discuss a specific example of an origami in genus 2, and to give an explicity algebraic description for the Teichmueller curve, which by construction is an analytic object. To this end, a summary of the theory of Riemann surfaces with focus on hyperelliptic surfaces, as well as an introduction to translation surfaces, Teichmueller curves and origamis is also included.