Density functional theory (DFT) calculations are used to explore water adsorption and activation on different a-Ga2O3 surfaces, namely (001), (100), (110), and (012). The geometries and binding energies of molecular and dissociative adsorption are studied as a function of coverage. The simulations reveal that dissociative water adsorption on all the studied low-index surfaces are thermodynamically favorable. Analysis of surface energies suggests that the most preferentially exposed surface is (012). The contribution of surface relaxation to the respective surface energies is significant. Calculations of electron local density of states indicate that the electron-energy band gaps for the four investigated surfaces appears to be less related to the difference in coordinative unsaturation of the surface atoms, but rather to changes in the ionicity of the surface chemical bonds. The electrochemical computation is used to investigate the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER) on a-Ga2O3 surfaces. Our results indicate that the (100) and (110) surfaces, which have low stability, are the most favorable ones for HER and OER, respectively.