Corrosion of nuclear fuel (UO2) leads to the formation of higher-order oxides up to U3O8. In order to study this oxidation, we investigate the adsorption of the O atom and oxygen-containing molecules (O2, H2O, H2O2) on the three most stable UO2 sur- faces ((111), (110), and (100)). The calculations are performed within DFT, using PBE+U including spin-orbit coupling and taking into account the non-collinear 3k (transverse) magnetic ground state. Dissociative adsorption is found for H2O and H2O2 on the (111) and (100) UO2 surfaces respectively, forming hydroxyl groups on the surface. Adsorption on the UO2 surface lowers the barrier to dissociation of O2. Defect formation energy is calculated for interstitial oxygen, up to several layers into the material starting from the surface. Diffusion energy barriers are presented. Adsorption energies are also studied as a function of temperature and partial pressure.