  This thesis describes the observation and study of Bose-Einstein condensation
of a trapped, dilute gas of atomic hydrogen. The condensate and normal gas are
studied by two-photon spectroscopy of the 1S-2S transition. We condense over
10^9 atoms per second for several seconds, and the peak condensate density is
around 5x10^15 cm^-3. Topics covered in the thesis include a theoretical
analysis of Bose-condensed hydrogen, a description of the cryogenic trapping
cell and the evaporative cooling techniques used to bring the gas to the
condensation point, and an analysis of the condensate.
