The Mars Odyssey Gamma-Ray Spectrometer is a suite of three different instruments, a gamma subsystem (GS), a neutron spectrometer, and a high-energy neutron detector, working together to collect data that will permit the mapping of elemental concentrations on the surface of Mars. The instruments are complimentary in that the neutron instruments have greater sensitivity to low amounts of hydrogen, but their signals saturate as the hydrogen content gets high. The hydrogen signal in the GS, on the other hand, does not saturate at high hydrogen contents and is sensitive to small differences in hydrogen content even when hydrogen is very abundant. The hydrogen signal in the neutron instruments and the GS have a different dependence on depth, and thus by combining both data sets we can infer not only the amount of hydrogen, but constrain its distribution with depth. In addition to hydrogen, the GS determines the abundances of several other elements. The instruments, the basis of the technique, and the data processing requirements are described as are some expected applications of the data to scientific problems