The nature of "dark matter" and the formation and evolution of galaxies, have emerged as key questions of contemporary cosmology. Redshift surveys of nearby galaxies reveal clouds of galaxies and voids on scales much larger than previously suspected, but cannot by themselves address how such structure arose. It has gradually become clear that galaxies have indeed evolved measurably within the last 3-7 billion years, but by how much and by what mechanisms is not known. Overlying all these concerns is uncertainty about the amount and nature of dark matter and how it impacts the development of galaxies and the growth of large-scale structure. Substantial gains have been made, but progress is discouragingly slow owing to the enormous observational difficulties attendant in studying the faintest galaxies. The advent of a new class of large ground-based telescopes - of which Keck is the first - will increase progress dramatically, and time is now ripe for a major new assault on these puzzles. The main need is first to clarify how much and what kind of evolution has occurred in galaxies over the last half of the lifetime of the Universe. The DEEP program (Deep Extragalactic Evolutionary Probe) will tackle these problems. Through DEEP, an understanding is sought of how their distribution in space has evolved over the last several billion years. The answers will certainly constrain the nature of the dark matter and, may allow us even to address the ultimate goal - the geometry of space itself. The heart of DEEP is a redshift survey of ~15,000 galaxies. A novel aspect of DEEP is the measurement of internal motions in galaxies, since these provide estimates of their mass. Evolution is thus revealed by comparing the properties of distant galaxies with their nearby, similar-mass counterparts. Very large samples are required to study separately the evolution among the known wide variety of galaxies. Clustering and the geometry of space are also problems that require large samples to be studied for confidence in the results. The overriding problem for such a program is the great amount of telescope time required to obtain high-quality spectra for exquisitely faint, distant galaxies. Heroic efforts with current spectrographs on 3-4 m class telescopes have resulted in just a few dozen redshifts at the very faint 24 magnitude limit of DEEP. The Keck Telescope with its first-generation spectrograph LRIS (Low Resolution Imaging Spectrograph) will be able to obtain such redshifts substantially faster - it may be practical to acquire some 600-700 galaxies per year with a large investment of time - but even so, 20-25 years would be required to obtain a sample of 15,000 galaxies. This is not practical. A new spectrograph for the Keck Telescope will provide dramatic gains in speed - 5 times over LRIS and 80 times or more over any current system. This spectrograph, the Multi-Barrel Survey Spectrograph (MBSS), utilizes a state-of-the-art wide-field camera that has already been incorporated into LRIS. Using a novel feature of the LRIS optics - an off-axis slit and matching collimator - the LRIS optical system will be replicated four times in a compact design with high efficiency to create an instrument ideally suited to the study of faint galaxies. The same spectrograph will also service a wide variety of the faintest survey programs besides DEEP. The issues that DEEP addresses - galaxies, large-scale structure, dark matter, and the evolution of the universe - are ones that strongly stimulate the public imagination. Since DEEP is being carried out in partnership with the Berkeley Center for Particle Astrophysics, the project is ideally placed to utilize its educational programs to reach out to a wide audience.