The Pd/a-Al2O3(0001) interface at low Pd coverage has been studied by a variety of theoretical methods and models at this metal-oxide interface. All results are consistent and predict a noticeable interaction dominated by the metal polarization in response to the presence of the substrate. A significant contribution of the charge transfer from the transition metal to the surface is also observed. The periodic fully relaxed calculations show that the most favorable adsorption site for the interaction of Pd with corundum involves the anionic surface sites, in particular the on-top oxygen site. It is also shown that adsorption of Pd atoms on the surface induces a significant relaxation of the aluminum oxide substrate, especially for the outermost aluminum layer. The small differences observed in the adsorption energies near the oxygen atoms suggest a high mobility of Pd atoms on the surface.