Abstract : The Time-dependent Hartree-Fock (TDHF) theory is applied to the study of heavy ion collisions at energies around the Coulomb barrier. The competition between fusion and nucleon transfer mechanisms is investigated. For intermediate mass systems such as 16O+208Pb, proton transfer favors fusion by reducing the Coulomb repulsion. A comparison with sub-barrier transfer experimental data shows that pairing correlations are playing an important role in enhancing proton pair transfer. For heavier and more symmetric systems, a fusion hindrance is observed due to the dominance of the quasi-fission process. Typical quasi-fission time of few zeptoseconds are obtained. Actinide collisions are also investigated both within the TDHF approach and with the Ballian-Vénéroni prescription for fluctuation and correlation of one-body observables. The possible formation of new heavy neutron-rich nuclei in actinide collisions is discussed.