Mars had outgassed at least 0.5 to 1 km of water, 10 to 20 bar of CO2, and 0.1 to 0.3 bar of N2. The volatiles that have been retained are mostly in the cratered uplands. Terrain softening, fretted channels, debris flows, and closed depressions indicate that at least the upper 2 km of the cratered uplands at high latitudes (>30??) contain ice in amounts that exceed the porosity, estimated to be 10-20%. Theoretical studies, and lack of these features in the cratered uplands at low latitudes, suggest that the upper 1 km of the uplands at low latitudes is ice poor. However, valley networks indicate that water was present near the surface early in the planet's history, although in amounts smaller than at high latitudes. The entire upper 1 km, planetwide is estimated to have contained 75-125 m of water at the end of heavy bombardment. The largest sink for water is the megaregolith below 1 km. Episodic eruption of water from the deep megaregolith cut many of the large outflow channels. From the volume of water needed to cut the circum-Chryse channels, and assuming uniform planetwide distribution of water, the deep megaregolith is estimated to have contained at least 350 m of water at the end of heavy bombardment, thereby giving a total minimum inventory of 424-475 m planetwide. Most of the water lost from the low-latitude uplands by diffusion and in cutting the valley networks is now believed to be in the polar layered terrains. Most of the water involved in cutting the outflow channels is in the low-lying northern plains where a variety of features that have been attributed to ground ice is present. A large fraction of the planet's surface has been overplated with water-poor volcanics, of which we have samples in the SNC meteorites. The younger volcanics have reacted extensively with the old volatile-rich basement. Some of the CO2 and N2 outgassed was lost during heavy bombardment by impact erosion of the atmosphere and other processes. The remaining was fixed carbonates and folded deep into the megaregolith during heavy bombardment. ?? 1986.