  We report first-principles calculations of the k- and T-dependent
superconducting gap Delta(k,T) in MgB2 and its manifestation in various
measured quantities. Because the Fermi surface has disconnected sheets with
different electron-phonon coupling strengths, our calculations show that near
T=0, the values of Delta(k) cluster into two groups: large values (about 6.5 to
7.5 meV) on the strongly coupled sheets and small values (about 1 to 3 meV) on
the weakly coupled sheets. The calculated gap, quasiparticle density of states,
and specific heat and their temperature dependences are in agreement with the
recent measurements which conclude that MgB2 is a multiple gap superconductor.
In fact, theory predicts four prominent values for the gap at low T.
