Neutron data observed using the Neutron Spectrometer aboard 2001 Mars Odyssey provide a lower limit to the global inventory of Martian water-equivalent hydrogen. Hydrogen-rich deposits ranging between about 20% and 100% water-equivalent by mass are found poleward of ¿50¿ latitude, and less rich, but significant, deposits are found at near-equatorial latitudes. The equatorial deposits between ¿45¿ latitude range between 2% and 10% water-equivalent hydrogen by mass and reach their maximum in two regions that straddle the 0-km elevation contour. Higher water abundances, up to ~11%, are required in subsurface regolith of some equatorial regions if the upper 10 g/cm2 of regolith is desiccated, as suggested on average by comparison of epithermal and fast neutron data. The hydrogen contents of surface soils in the latitude range between 50¿ and 80¿ north and south are equal within data uncertainties. A lower-limit estimate of the global inventory of near surface hydrogen amounts to a global water layer about 14 cm thick if the reservoir sampled from orbit is assumed to be 1 m thick.