It is proposed that the scattering of positrons and electrons by atoms and molecules be studied experimentally in order to learn more about basic interactions of antimatter with matter. The proposed research includes measurement of total, differential, and inelastic scattering of positrons by atoms and molecules, as well as a search for positron scattering resonances. An important part of the research program is to make corresponding electron scattering comparison measurements in the same apparatus using the same technique. Information will be obtained that is of interest in many areas of science and technology. For example, the scattering of positrons by atomic and molecular hydrogen is of importance to astrophysicists for the interpretation of positron annihilation gamma rays observed in solar flares and in the central region of our galaxy.