We report maps of the concentrations of H, Si, Cl, K, Fe, and Th as determined by the Gamma Ray Spectrometer (GRS) on board the 2001 Mars Odyssey Mission for ±∼45° latitudes. The procedures by which the spectra are processed to yield quantitative concentrations are described in detail. The concentrations of elements determined over the locations of the various Mars landers generally agree well with the lander values except for Fe, although the mean of the GRS Fe data agrees well with that of Martian meteorites. The water-equivalent concentration of hydrogen by mass varies from about 1.5% to 7.5% (by mass) with the most enriched areas being near Apollinaris Patera and Arabia Terra. Cl shows a distribution similar to H over the surface except that the Cl content over Medusae Fossae is much greater than elsewhere. The map of Fe shows enrichment in the northern lowlands versus the southern highlands. Silicon shows only very modest variation over the surface with mass fractions ranging from 19% to 22% over most of the planet, though a significant depletion in Si is noted in a region west of Tharsis Montes and Olympus Mons where the Si content is as low as 18%. K and Th show a very similar pattern with depletions associated with young volcanic deposits and enrichments associated with the TES Surface Type-2 material. It is noted that there appears to be no evidence of significant globally distributed thick dust deposits of uniform composition.