The atomic hydrogen maser is described. In this device hydrogen atoms in the upper hyperfine state are focused onto the entrance aperture of a Teflon coated quartz bulb in which the atoms are stored for about a second. This bulb is surrounded by a cylindrical radiofrequency cavity; When the cavity is tuned to the hyperfine frequency of atomic hydrogen, maser radiation is produced. Due to the large line Q resulting from the long storage time, the radiation is highly stable in frequency. Results are given of theoretical calculations on the threshold flux of atoms required for maser oscillations, on the various relaxation processes that limit the effective storage time and on the possible sources of frequency shifts of the maser. Results are given on the relative stability of two hydrogen masers.