Mars Global Surveyor (MGS) radio science comprises studies of the atmosphere and gravity of the planet. Perturbations of the 3.6-cm λ radio path by the atmosphere during periods of atmospheric occultation provide the vertical temperature-pressure structure T to accuracies at the surface of ΔT≈0.4 K and Δp≈2 Pa, and ~10 K and ~0.6 Pa at altitudes of 40--50 km; the error in radius is Δr≈1 m at all levels. Accurate knowledge of the radius permits fixing of the T-p structure to the geopotential and use of the gradient wind equation to calculate components of the wind. Systematic sampling of the atmosphere in combination with the accuracy of the MGS radio system supports studies of the large-scale dynamics of the atmosphere, including seasonal variations of the atmospheric fields and embedded waves such as Kelvin and Rossby waves. Terminator region ionospheric electron density profiles are obtained successfully much of the time but on occasion are undetectable with the MGS system. Two-way radio tracking of MGS with uncertainties in the line-of-sight velocity of several to tens of μm s-1 and less supports solution for spherical harmonic models of the gravity field of order and degree in the range of 75¿75, although the degree and order of meaningful terms is limited by the ~400 km spacecraft altitude to ~62¿62, corresponding to a resolution of a few degrees of arc on the surface. This resolution of gravity is sufficient to support geophysical studies of the planet's interior structure and history. Additional radio science investigations include the search for gravitational radiation and observation of very low grazing angle forward scattering by the surface of Mars. ¿ 2001 American Geophysical Union <