Global distributions of thermal, epithermal, and fast neutron fluxes have been mapped during late southern summer/northern winter using the Mars Odyssey Neutron Spectrometer. These fluxes are selectively sensitive to the vertical and lateral spatial distributions of H and CO2 in the uppermost meter of the martian surface. Poleward of +/-60 degrees latitude is terrain rich in hydrogen, probably H2O ice buried beneath tens of centimeter-thick hydrogen-poor soil. The central portion of the north polar cap is covered by a thick CO2 layer, as is the residual south polar cap. Portions of the low to middle latitudes indicate subsurface deposits of chemically and/or physically bound H2O and/or OH.