Professor Dehmelt proposes to continue his studies of single elementary particles at rest in free space. The main thrusts of this Nobel Prize winning work are (1) Investigate the possibility that electrons and positrons have internal structure, (2) Test the theory of Quantum Electrodynamics to the limits of the physically measurable, (3) Test electron-positron mirror symmetry and the hypothesis that the combination of charge, parity, and time is a conserved quantity in nature.