We present detailed evolutionary calculations for carbon - oxygen - and helium - core white dwarf models with masses ranging from M = 0.1 to M = 1.2 M⊙ and for metallicities Z = 0.001 and Z = 0. The sequences cover a wide range of hydrogen envelopes as well. We have taken finite - temperature effects fully into account by means of a detailed white dwarf evolutionary code, in which updated radiative opacities and equations of state for hydrogen and helium plasmas are considered. The energy transport by convection is treated within the formalism of the full - spectrum turbulence theory, as given by the self - consistent model of Canuto, Goldman and Mazzitelli. Convective mixing, crystallization, hydrogen burning and neutrino energy losses are taken into account as well. The set of models presented here is very detailed and should be valuable, particularly for the interpretation of the observational data on low - mass white dwarfs recently discovered in numerous binary configurations and also for the general problem of determining the theoretical luminosity function for white dwarfs. In this context, we compare our cooling sequences with the observed white dwarf luminosity function recently improved by Leggett, Ruiz & Bergeron and we obtain an age for the Galactic disc of ≈ 8 Gyr. Finally, we applied the results of this paper to derive stellar masses of a sample of low - mass white dwarfs.Facultad de Ciencias Astronómicas y Geofísicas