  The pseudogap phenomena in High-$T_{{\rm c}}$ cuprates are investigated on
the basis of the Hubbard model which includes only the on-site repulsive
interaction $U$. We consider the pairing scenario for the pseudogap. The
pseudogap arises from the resonance scattering due to the strong
superconducting fluctuations.
  First, the electronic state and the anti-ferromagnetic spin fluctuations are
calculated by using the FLEX approximation. The T-matrix (the propagator of the
superconducting fluctuations) is calculated by extending the $\acute{{\rm
E}}$liashberg equation. The self-energy due to the superconducting fluctuations
is calculated by the T-matrix approximation. The pseudogap is shown in the
single particle properties and the magnetic properties by the microscopic
calculation. A comprehensive explanation of the doping dependence of the
pseudogap is obtained. Furthermore, we apply the theory to the electron-doped
cuprates and obtain the consistent results with the recent experiments.
Finally, the self-consistent calculation for the spin fluctuations,
superconducting fluctuations and the single particle properties are carried out
within the FLEX and the self-consistent T-matrix approximations. The calculated
superconducting critical temperature $T_{{\rm c}}$ is remarkably reduced from
the results of the mean field (FLEX) calculation. It is shown that the critical
temperature decreases with decreasing doping in the under-doped region with
large $U$.
