The focus of this thesis is the study of the surface properties of certain transition metal oxides which are already used in SOFCs. Density functional theory (DFT) has shown its ability to provide a good description of both bulk and surface properties of many materials and is the main tool used to further the understanding of the studied materials. Here, it was used as the workhorse method to provide an atomistic understanding of the surface properties of transition metal oxides. In all cases, the comparison with accompanying experiments conducted by various partnering groups highlights the viability of such an approach. In the first part of this work, the adsorption of ultra-thin films of Zirconia (ZrO2) on the (111) surfaces of metal substrates like pure Platinum and alloys of Platinum and Palladium containing Zirconium (Pt3Zr, Pd3Zr) was studied. In the simulations, the oxide-metal interface was modelled in unit cells of increasing complexity. The smallest unit cell consisted of one 3 ZrO2 unit cell on top of a single surface unit cell of Pt3Zr/Pd3Zr. Despite the large lattice mismatch and strain on either film or substrate, the resulting buckling of 43pm and 73pm yields good agreement with the experimental value of 50pm and 100pm for Pt3Zr and Pd3Zr, respectively. To better describe the real unit cell, further simulations using larger (1919)R23.4 model cells with both pure Pt and Pt3Zr substrates were done. It turned out that the lattice match which is governed by the lattice constant of the oxide film plays a decisive role in the stability of the oxide film. Next, the previously described model cells were used to study the adsorption of various metal adatoms (Au, Ag, Pd, and Ni) and water molecules in comparison to adsorption on ZrO2 bulk. On the bulk ZrO2 surfaces, the simulations yield weak adsorption for Ag, followed by Au and stronger adsorption for Pd and Ni. On the ultra-thin ZrO2 films, Au and Ni bind more strongly. Also, Ag, Au, and Ni show charging effects on the ZrO2 film by electron transfer to (Au) and from (Ag, Ni) the metallic substrate. The water molecule prefers dissociative adsorption on both bulk and ultra-thin ZrO2 surfaces with predicted adsorption energies of about -1.3eV and -1.0eV, respectively. This value is defined by the accessibility of the surface Zr and the presence of under-coordinated O atoms at the surface. At increased water coverage the dissociated H2O serve as nucleation sites where additional intact water molecules are bound by additional hydrogen bonds to the formed OH. The second part of this work focused on the bulk and surface properties of two Ruddelsden-Popper ternary oxides, strontium and calcium ruthenate (Sr3Ru2O7 and Ca3Ru2O7). In particular, the adsorption of water and oxygen molecules was studied. In experiments, both can be cleaved very easily along the (001) plane and form well-ordered surfaces with AO (A = Sr, Ca) termination. Even though they exhibit a similar stoichiometry, the size of the A-site cation leads to decisive differences in the bulk and surface structures. In Sr3Ru2O7, the ruthenium atom at the B-site is located at the centre of octahedra formed by the surrounding oxygen atoms which are rotated along the (001) axis. The smaller ionic radius of the calcium atoms in Ca3Ru2O7 leads to both rotation and tilting of these octahedra. Water prefers dissociative adsorption on both perovskite surfaces. The adsorption energy predicted by the van-der-Waals corrected optB86b functional for low coverage is 1.26eV and 1.64eV for Sr3Ru2O7 and Ca3Ru2O7, respectively. The dissociated water molecule prefers adsorption at cation-cation bridge sites with the split-off hydrogen forming a surface hydroxyl with the apical oxygen of a nearby octahedron. The residual OH then forms a hydrogen bond to this surface hydroxyl. On the Sr3Ru2O7(001) the singular adsorbed water molecule shows a small activation energy of 169meV, enabling the residual (OH)ads to hop to the next Sr-Sr bridge site. On the Ca3Ru2O7(001), the lower symmetry of the surface prohibits a similar behaviour. At higher coverage, the H2O form dimers and line structures on both surfaces. Oxygen molecules adsorb in an undissociated configuration at cation bridge sites on both Sr3Ru2O7(001) and Ca3Ru2O7(001) with adsorption energies at low coverage of about 1.4 eV calculated with the optB86b functional. At high coverages, the adsorption energy is reduced to 0.9 eV and 1.2 eV for the strontium and calcium ruthenates, respectively. In all cases, the calculations predict adsorption as a charged superoxo molecule (O2) with the additional charge originating from the metallic properties of the oxide substrate. Due to an underestimation of the HOMO-LUMO gap of the superoxo species DFT yields artificially increased adsorption energies. Many-electron RPA total energy calculations predict adsorption energies of -1.0eV and -0.7eV, respectively, in much better agreement with the experiment.