There are two major focal points of this research. The first focal point is the use of fast atomic beam radiofrequency spectroscopy to measure with high precision the fine structure of H and He+. These measurements will be used to provide fundamental tests of quantum electrodynamics and to provide an independent precise value for the fine structure constant. A second focal point is the study of the triplet Rydberg states of the hydrogen molecule through a molecular beam-laser spectroscopy technique in which metastable molecules produced by electron bombardment are excited to high lying Rydberg states through radiation from a single uv laser or from two lasers via a resonant intermediate state. The goal is to study the structure of the energy levels and the mechanism for decay by autoionization, predissociation, and emission of radiation.