The Epoch of Reionization is one of the most active areas of research in astronomy because of its importance in the history of the Universe. Numerous studies are currently probing the redshifts at which we believe this reionization to have occurred (z =6 - 15) in search of the first galaxies, which / produced. the ionizing radiation responsible for the transition from a neutral intergalactic medium. These sources are believed to have strong emission in the Lyman alpha line. In this thesis, work carried out on a survey making use of gravitational lensing to search for Lyman alpha emitting galaxies between z =7 and 11 is presented. Gravitational lensing is a very powerful tool in the search for extremely high redshift sources since it allows observers to detect sources too faint to be detected by conventional unlensed means. Archival data from the ISAAC facility on the Very Large Telescope has been rigorously reduced and analysed using the principle of matched filters. Unfortunately no extremely high redshift candidates have been detected but three low redshift (z =1.68, 1.41 and 1.16) galaxy candidates have been observed. Mapping the magnification afforded by gravitational lensing has allowed the estimation of possible luminosity functions, which have been compared against the work of contemporary Lyman alpha surveys. This thesis has a detailed description of all the data obtained, the reduction technique used, the matched filter detection algorithm and analysis into the possible luminosity function with special interest paid to the advantages afford by gravitational lensing.