Todays, antenna gain, efficiency and bandwidth enhancement are important engineering goals. In order to achieve these goals, using lenses in antenna structure is one of the interesting and common methods. Traditional lenses have been made from condensed materials and currently are less used because of drawbacks such as heavy weight and volume. Therefore much studies and researches have been done to replace traditional lenses with thin, lightweight, low cost and high efficiency lenses. A metasurface is an appropriate choice to realize a flat lens antenna. In this thesis, the introduction of traditional lenses is discussed first. Then, different types of alternative structures such as artificial dielectric lenses, transmit arrays and phase shifting surfaces are introduced. After that the metasurface performance is analyzed and a two dimentional Luneburg lens consist of rectangular unit cells based on metasurface is analyzed, designed and simulated. This lens antenna is located in front of a microstrip patch antenna. According to results, using the lens increases the gain, efficiency and bandwidth of patch antenna. Finaly, by optimizing the dimentions of unit cells, a low profile flat lens is designed and simulated. Using this lens increases the gain of the patch antenna. Keywords 1-Metasurface 2-Lens antenna 3-Luneburg le 4-GRIN function