The dating of the Universe is one of the major tasks faced by modern astrophysics. In particular, "nucleo-cosmochronology" aims at determining the age of the nuclides through the use of measured abundances (in old stars or meteorites) of radio nuclides with lifetimes commensurable with presumed lifetimes of the galactic disc. Such nuclides, mainly the long-lived actinides, are produced by the rapid neutron-capture process (or r-process) of nucleosynthesis. A reliable prediction of the actinide production ratios requires continuous efforts to improve the predictions of the nuclear properties involved. These concern the ground and excited state properties (nuclear masses, fission barriers and level densities) , as well as the strong, electromagnetic and weak interaction properties of all the nuclei synthesized during the r-process. These nuclei are so neutron-rich that there is no hope of being able to measure them in the laboratory. It is thus of paramount importance to make reliable extrapolations of these quantities out towards the neutron drip line. The aim of the project is to put the extrapolations on as rigorous a footing as possible by treating all nuclear aspects of the astrophysical r-process on a unified microscopic basis. This involves (i) the extension of the Hartree-Fock method, recently developed to calculate nuclear masses, to the calculation of fission barriers for all nuclei involved in the r-process, (ii) the determination of fission rates, including spontaneous, neutron-induced and beta-delayed fission processes, on the basis of microscopic models, and (iii) the analysis of the impact of the newly-derived fission rates on the r-abundance predictions, and more particularly on cosmochronological predictions .