A great mystery of the Universe is how the first stars and galaxies formed. Astrophysicists can virtually look back in time by examining some of the most distant galaxies in the Universe, whose light has taken billions of years to reach Earth. Detailed, careful study of these very distant galaxies is critical to understanding how the first stars and galaxies formed. Unfortunately, it is very challenging to identify these galaxies. This project aims to use a new technique that exploits gravitational lensing by foreground clusters of galaxies that magnify these distant galaxies, making them easier to detect. The principal investigators' (PIs') new theoretical framework for analyzing multiple-lensing planes reveals that there are mass distributions consisting of multiple structures along the line-of-sight and large integrated masses that produce a many-fold increase in the number of lensed z > ~7 sources, particularly at the faint end of the galaxy luminosity function. These beams are effective because they create significant magnification over a large area, or high etendue. Cosmological simulations suggest that they are rare but identifiable by choosing lines-of-sight with the highest integrated luminosities of galaxies that trace the densest structures, i.e., luminous red galaxies. The PIs have now identified 40 such lines-of-sight in the Sloan Digital Sky Survey (SDSS). Spectroscopy of the first seven confirms that they are likely the most powerful gravitational lens telescopes in the sky. This project will use a comprehensive observational and theoretical program to enable highly efficient ground- and space-based follow-up surveys for lensed z ~ 7 to 10 sources. Using galaxy spectroscopy and lensed arc imaging to constrain each line-of-sight mass distribution, coupled with theoretical modeling to generate a precise lensing magnification map, the PIs will place the first limits on the faint end luminosity evolution of the most distant galaxies. This work will advance the training of graduate students at The University of Arizona and Rutgers University by allowing them to work with senior personnel on forefront observational analyses and theoretical modeling. Co-PI Zabludoff is involved in The University of Arizona's Women in Science and Engineering (WISE) chapter, where she discusses her research in their workshops for teenage girls. She will also talk about astronomy research and careers with members of the Tohono O'odham Nation and with students in local schools. Co-PI Keeton is the Faculty Director of the Aresty Research Center for Undergraduates at Rutgers, a privately-endowed center that supports approximately 200 student research projects each year. This project will enhance the infrastructure for research and education via the co-PI's partnership, advance the teaching of faculty and the training and learning of students, broaden the dissemination of knowledge through the public release of the lens modeling software, and may increase the participation of underrepresented women and Native Americans through outreach.