Aluminum hydroxides are the precursors of metastable aluminas which are used in many applications in industrial catalysis. They constitute a starting point for the understanding of transition processes and structures of metastable transition aluminas. Using first-principle density functional calculations, several polymorphs with different degrees of hydration are simulated: gibbsite, bayerite, diaspore, boehmite, and tohdite. Optimized structures, including cell parameters, atomic positions, and space groups, are calculated and compared with experimental crystallographic data. In some cases, polymorphic structures were found with different orientations for the hydrogen bonds. The study of thermodynamical stability as a function of temperature allows to point out the main tendencies: the higher the temperature, the lower is the degree of hydration of the thermodynamical stable species. Furthermore, calculated limiting temperatures of stability of the various polymorphs are predicted and compared favorably with experimental data available on the transition temperatures.