Positronium, with the chemical symbol Ps, is a very light form of hydrogen atom consisting of an electron and an anti-electron, or positron. Being composed of equal amounts of matter and antimatter, the longest-lived ground state of positronium lives for only one seventh of a microsecond before annihilating into three photons. Nevertheless, this transient existence is long enough for studying the properties of a dense gas of positronium atoms. This research will employ a dense positronium gas to investigate di-positronium molecules, Ps2, and positronium Bose-Einstein condensation. An apparatus developed with the assistance of an NSF Instrumentation program grant (DMR-0216927) will provide this project with short pulses containing about 100 million positrons. The positrons will be focused on a target surface composed of a porous solid in which positronium atoms form with high probability. The target will contain a tiny buried cavity into which one million positronium atoms will collect to a density such that positronium Bose-Einstein condensation should occur at temperatures as high as 20K. To observe these effects, a pulsed laser system will deliver ultra-violet light capable of exciting the positronium and Ps2 Lyman-alpha, or ground-state to first excited state, transitions. Although a Ps cavity would be transparent to the ultra-violet light when filled with an ordinary gas of positronium atoms, the cavity will become opaque when the atoms condense, thus enabling the first observations of positronium Bose-Einstein condensation. The broader impact of the program involves student training as well as outreach to the local high school.