Solar cells are at the frontier of renewable energy technologies. Photovoltaic energy is clean, reusable, can be used anywhere in our solar system and can be very well integrated with power distribution grids and advanced technological systems. Thin film solar cells are a class of solar cells that offer low material cost, efficient fabrication process and compatibility with advanced electronics. However, as of now, the conversion efficiency of thin film solar cells is inferior to that of thick crystalline cells. Research efforts to improve the performance bottlenecks of thin film solar cells are highly motivated. A class of techniques towards this goal is called light trapping methods, which aims at improving the spectral absorptivity of a thin film cell by using surface texturing. The precise mathematical and physical characterization of these techniques is very challenging. This dissertation proposes a numerical and computational framework to optimize, design, and fabricate efficient light trapping structures in thin film solar cells, as well as methods to verify the fabricated designs. The numerical framework is based on the important "inverse optimization" technique, which is very is widely applicable to engineering design problems. An overview of the state-of-the-art thin film technology and light trapping techniques is presented in this thesis. The inverse problem is described in details with numerous examples in engineering applications, and is then applied to light trapping optimization. The proposed designs are studied for sensitivity analysis and fabrication error, as other aspects of the proposed computational framework. At the end, reports of fabrication, measurement and verification of some of the proposed designs are presented.