Explore the fascinating evolution of water on Mars in this comprehensive lecture. Delve into the estimated Martian inventory of H2O, debates on early Mars climate, and potential evolution of the Martian hydrosphere. Examine Mars thermal history models, the nature of the Martian crust, and evidence of impacts into water-rich or ice-rich surfaces. Investigate inferred hydraulic conditions during different geological periods, potential paleoshorelines, and the distribution of valley networks suggesting a northern ocean. Learn about ice instability at low latitudes, potential recharge of subpermafrost groundwater, and geomorphic evidence of polar basal melting. Gain insights into the freezing of a Martian ocean and the thickening of the cryosphere, allowing for the rise of a global water table.