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The discovery of superconductivity in MgB2, with a rather high transition temperature, has triggered a large number of theoretical and experimental investigations on important issues such as, e.g., the role of gap anisotropy over the Fermi surface (multi-gap superconductivity). We report here the results obtained in this compound using the density functional theory for superconductors, recently proposed by the authors. Without invoking any adjustable parameters, such as μ∗, we obtain the transition temperature, the gaps, and the specific heat in very good agreement with experiment. Moreover, our calculations allow for a detailed study of how the phonon-mediated attraction and Coulomb repulsion act differently on σ and π states, thereby stabilizing the observed superconducting phase.