The next generation of telescopes will be able to directly measure the light curves of exoplanets. This thesis demonstrates the potential of using light curve analysis to study exoplanetary ring systems, with the goal of retrieving their albedo map and optical depth. This can improve our understanding of the composition, formation, and evolution of such systems. We construct a mathematical model that describes how light interacts with ring particles through absorption, transmission, and scattering. Applying this model to data of Saturn’s rings from high-resolution images by NASA's Cassini space probe, albedo maps for the rings are constructed and the optical depth is found to be mostly consistent with existing literature. We then derive an analytic formula for the light curve of an exoplanetary ring system. This formula is converted into a numerical linear transformation that links the albedo map of a ring system to its light curve. Using the Moore-Penrose pseudoinverse and singular value decomposition this transformation is inverted, enabling the retrieval of the albedo map from the light curve. The method is tested using synthetic data of model ring systems while varying the axial tilt, observer direction, and signal-to-noise ratio from artificial Gaussian white noise. The results show that the method is generally effective at recovering the albedo map and optical depth for signal-to-noise ratios down to 10³.