  The unique Fermi surfaces and their nesting properties of Sr2RuO4 are
considered. The existence of unconventional superconductivity is shown
microscopically, for the first time, from the magnetic interactions (due to
nesting) and the phonon-mediated interactions. The odd-parity superconductivity
is favored in the $\alpha$ and $\beta$ sheets of the Fermi surface, and the
various superconductivities are possible in the $\gamma$ sheet. There are a
number of possible odd-parity gaps, which include the gaps with nodes, the
breaking of time-reversal symmetry and $\vec{d}\parallel \hat{z}$.
