We discuss the origin of the unconventional superconductivity in a Hubbard model. The origin of the unconventional superconductivity is considered to be a wave number dependence of a quasi particle interaction, which is induced by the Coulomb interaction U. Using the third order perturbation theory with respect to U, we discuss the wave number dependence induced by spin fluctuations and vertex corrections. We investigate the pairing states for the various lattice structures in the Hubbard model and we point out the important factors in the origin of the singlet and triplet superconductivities.

PACS numbers: 74.20.Rp, 71.10.Fd