First-principles calculations have been carried out to investigate the structure, stability, and finite-temperature thermodynamic properties of the key precipitates in the Al-Mg-Si alloys including beta aEuro(3)-Mg(5)Si(6), U1-Al(2)MgSi(2), U2-Al(4)Mg(4)Si(4), beta'-Mg(9)Si(5), and beta-Mg(2)Si. The calculated phonon densities of states indicate that these precipitated phases are vibrationally stable. Within the framework of the quasiharmonic approach, the finite-temperature thermodynamic properties of these precipitated phases including entropy, enthalpy, and Gibbs free energy have been calculated. The heat capacities at constant pressure for these precipitates are predicted. The finite-temperature entropies of formation, enthalpies of formation, and Gibbs free energy of formation for these precipitates are also computed. The acquired thermodynamic properties are expected to be utilized for the prediction of the metastable equilibria in the Al-Mg-Si alloys.