Quantum mechanical approaches to selecting the most accurate method of calculation for the bulk structure of alpha-alumina. The aluminium terminated {0001} surface is then fully analysed, followed by the hydroxylated {0001} alpha-alumina surface, formed by the Dissociative chemisorption of water. This is then followed by the energetically favourable chemisorption of hydrogen fluoride onto the clean {0001} alpha-alumina surface in a 1-2 mode via the Al-F and O-H interactions and the molecular physisorption of water onto the {0001} alpha-alumina surface. These density functional theory results are completed by the simulations of the stable surfaces of beta-alumina, the investigation into the hydroxylated {101} beta-alumina surface and the beta-AlF 3 {100} surface.