Abstract
A two-band model of MgB2 superconductivity is developed. It exploits repulsive σ-π interband coupling besides the σ-intraband electron-phonon attraction and Coulomb interaction. With an adjustable set of parameters the observed dependences of the gaps, specific heat and second critical magnetic field on temperature, furthermore Tc vs. Al-doping, and the Tc isotope effect exponent are reproduced without further fittings. The unconventional MgB2 superconductivity can be ascribed to the specific band structure and the role of electron interactions.