It is now well established that much of the Universe is composed of nonluminous matter, but there is little or no evidence for what this material might be. Certain galaxies (dwarf spheroidal galaxies) are the most local external systems thought to contain dark matter, and are the simplest type of galaxy. They contain little or no gas and have had relatively simple star formation histories. Careful kinematic studies of these galaxies may provide the least ambiguous evidence for the nature of dark matter. The research to be supported by this grant will measure precise velocities of stars in three dwarf spheroidal galaxies in order to measure the velocity dispersion of the stars in these systems. The acquisition of precise velocities in each of these systems will allow the gravitational potential of these galaxies to be measured. The precise structure of these galaxies is rather poorly known, and photometry will be obtained which will substantially improve our knowledge of the structure of these low luminosity galaxies.