We present a study of the stability of n-vacancies (Vn) and hydrogens in the hexagonal close-packed titanium system computed by means of first-principles calculations. In this work, performed by using the generalized gradient approximation of density functional theory, we focused on the formation energies and the processes of migration of these defects. In the first part, the calculated formation energy of the monovacancy presents a disagreement with experimental data, as already mentioned in the literature. The activation energy is underestimated by almost 20%. The stability of compact divacancies was then studied. We show that a divacancy is more stable than a monovacancy if their migration energies are of the same order of magnitude. We also predict that the migration process in the basal plane of the divacancy is controlled by an intermediate state corresponding to a body-centered triangle(BO site). The case of the trivacancies is finally considered from an energetic point of view. In the second part, the insertion of hydrogen and the processes of its migration are discussed. We obtain a satisfactory agreement with experimental measurements. The chemical nature of the interactions between hydrogen and titanium are discussed, and we show that the H-atom presents an anionic behavior in the metal. The trapping energy of hydrogen in a monovacancy as a function of the number of hydrogen atoms is finally presented.