The Lyman Far Ultraviolet Spectroscopic Explorer mission will obtain high resolution spectra (R 30,000) in the 912–1200 Å region with sufficient sensitivity to study faint sources throughout the galaxy and at large extragalactic distances. This spectral region provides unique tools for solving problems in cosmology (e.g. deuterium), galactic structure and evolution (e.g. O VI and H2), stellar evolution (e.g. O VI) and planetary science (e.g. H2). Recent advances in optical and detector technology, which make this goal possible with a moderate size experimental package, also enable the spectral coverage to extend down to 100 Å with good sensitivity and only a minimal increase in complexity. Thus a secondary goal is to cover the 100–912 Å region with moderate spectral resolution. In 1989, following a Phase A study of the mission concept, NASA selected the mission for Phase A study in 1989. Both Canada and the United Kingdom are participating in the definition and development of the mission.