This thesis develops a method to map the surface of an exoplanet. The problem of exoplanet mapping sounds easy to solve. Take a few photographs of an exoplanet and sew them together to create a map of the surface. The telescope required to do this is far beyond our technological capabilities. However, our current telescopes could allow us to measure the light reflected from the star on the surface of the star as a point source. This thesis constructs the surface map of an exoplanet using only a point source of reflected light as information. This method of planet mapping is called spin-orbit tomography, introduced by Cowan and Agol [2008] and more in depth by Fujii and Kawahara [2012]. Spin Orbit tomography is a method to construct a surface map from the reflected light curve, the total intensity of the light from the star, reflected on the surface of the planet, directed towards an observer.