The unique Fermi surfaces and their nesting properties of Sr2RuO4 are consi
dered. The existence of unconventional superconductivity is demonstrated fo
r the first time, by magnetic interactions (due to nesting) and phonon-medi
ated interactions. Two possible mechanisms of spin-triplet superconductivit
y are pointed out: one is due to the quasi-1D nature of the alpha and beta
sheets of the Fermi surface and other is due to the anisotropy of antiferro
magnetic (AF) fluctuations. The odd-parity superconductivity is favored in
the alpha and beta sheets of the Fermi surface, and various superconductivi
ties are possible in the gamma sheet. There area number of possible odd-par
ity gaps, which include the gaps with nodes, the breaking of time-reversal
symmetry and d parallel to(z) over cap.