The present thesis is devoted to the study of 3d-transition-metal monoxides in the frame-work of self-interaction corrected density functional theory using the local spin-density approximation (SIC-LSDA-DFT). In particular, the magnetic properties of bulk-NiO and a NiO(001) surface are discussed, the electronic structure of a NiO(001) is determined and the influence of vacancies in MnO and NiO is studied. The magnetic properties are characterised quantitatively by exchange-coupling constants of a Heisenberg-Hamiltonian incorporating nearest and next-nearest neighbours in the cation sublattice. The determined exchange-coupling constants are in very good agreement with those extracted from experimental data. Further, the change of coupling constants in the vicinity of the surface has been determined. Within the surface the coupling is decreased, while the coupling from the surface into the bulk material is increased when comparing to the respective bulk values. The electronic structure calculations for the NiO(001) surface reveal surface states due to symmetry breaking at the top of valence band having predominantly oxygen pz-like character, and at the bottom of the conduction band having predominantly Ni-d3r²-z²-like character. The influence of vacancies in MnO and NiO has been studied. A vacancy concentration of 3% on one sublattice of the antiferromagnets leads in both cases to half-metallic behaviour. In particular, for NiO a half-metallic state with vanishing macroscopic magnetisation ("half-metallic antiferromagnet") is obtained which might have technological importance.