Mountain glaciers and ice caps will melt and locally disappear due to climate warming. Projecting the impact on sea level rise, water resources and the living world requires an inventory of the current volume and distribution of glacier ice on Earth. My PhD project aims to provide this information by using novel inverse modelling algorithms which yield ice thickness maps (and thus ice volume) for all >200,000 glaciers in the world. The bulk of these simulations have been carried out. However, it is expected that more runs will need to be done in the review process. In addition, follow-up studies are planned which built on the output from the inversions. Consequently, we still need Alvis resources, although fewer hours than before.