The purpose of this paper is to study the evolution of Titan from the primordial core overturn to the present, and to investigate the possible existence of both a deep liquid layer and an iron core, depending on the composition of chondrites and the primordial amount of volatiles included in ices. Models of Titan's interior are constructed using theoretical models based on thermal and mechanical properties of ices and silicates. Depending on both the heat transfer efficiency in chondrites and ices, and the amount of heat present in the interior, many properties of the deep structure of the satellite are deduced. Heat transfer through the convecting shell in planets is commonly estimated using parameterized laws which relate the vigor of convection to the heat flux at the top of the convecting shell. These laws, established from studies with constant viscosity fluids have been changed in order to take into account the very large viscosity contrasts in the different layers. Models also require a good knowledge of both thermodynamic and rheological parameters of materials at high pressure. In Titan, many volatiles were probably present in the primordial liquid layer. These volatiles must decrease the freezing temperature of the liquid which is of fundamental importance for the evolution of the satellite. Recent experimental results on the system NH 3-H 2O are included in the present models. Evolution of the core - Using numerical models incorporating recent results on thermal convection for fluids with strongly temperature dependent viscosity, the thermal evolution of Titan's core is presented for two possible compositions of the planetoids. In the first case, the chondritic part of the planetoids was possibly composed of CI chondrites and the core is simply composed of silicates, whereas in the second case, chondrites with a large amount of metallic iron (EH enstatite chondrites) were accreted during Titan's formation. Diffusive heating increases the averaged temperature of the homogeneous chondritic core up to a critical value where marginal convection may occur about 1 Ga after the core overturn. In case 1, the onset of convection is accompanied by partial melting of the silicate core. Then, the vigor of convection keeps increasing and would still be vigorous at the present time. Partial melting of silicates below a thick thermal boundary layer at the top is very likely at present. In the other model (case 2), metallic iron starts melting before the onset of convection and implies a rapid overturn of the chondritic core into a layered structure with a dense liquid iron core surrounded by a silicate layer. In this layered core, convection in the silicate layer is not very vigorous, but probably still exists. Evolution of the icy layers - Radiogenic heating of silicates is transferred by convection through the ice shell. If convection is vigorous, the heat flux through the ice shell is larger than the heat flux from the core and crystallization in the liquid shell occurs both at the top and at the bottom. Then, two different evolutions can be expected: (i) the decrease of temperature due to thickening is small and the Rayleigh number of the ice I shell increases when the layer thickens (pure H 2O case). Freezing of the liquid layer is very rapid and Titan is presently composed of a thick icy mantle, which convects vigorously; and (ii) the freezing temperature decreases strongly when pressure increases so that the Rayleigh number does not increase when ice I thickens because viscosity increases rapidly (NH 3-H 2O case). As a consequence, the thickening of ice I is very slow. The present structure of Titan depends on the primordial composition of the liquid layer, but it is probable that a liquid layer, which could be more than 350 km thick, still exists in the interior of the satellite. Such a layer may be determined by the Cassini measurements.