  The anomalous properties of High-$T_{{\rm c}}$ cuprates are investigated both
in the normal state and in the superconducting state. In particular, we pay
atte ntion to the pseudogap in the normal state and the phase transition from
the pse udogap state to the superconducting state.
  The pseudogap phenomena observed in cuprates are naturally understood as a
precursor of the strong coupling superconductivity. We have previously show n
by using the self-consistent T-matrix calculation that the pseudogap is a resu
lt of the strong superconducting fluctuations which are accompanied by the
stron g coupling superconductivity in quasi-two dimensional systems [J. Phys.
Soc. Jpn . {\bf68} (1999) 2999.].
  We extend the scenario to the superconducting state. The close relation
between the pseudogap state and the superconducting state is pointed out. Once
t he superconducting phase transition occurs, the superconducting order
parameter rapidly grows rather than the result of BCS theory. With the rapid
growth of the order parameter, the gap structure becomes sharp, while it is
remarkably broad in the pseudogap state. The characteristic energy scale of the
gap does not chan ge. These results well explain the phase transition observed
in the spectroscopi c measurements.
  Further, we calculate the magnetic and transport properties which show the
pseu dogap phenomena. The comprehensive understanding of the NMR, the neutron
scatter ing, the optical conductivity and the London penetration depth is
obtained both in the pseudogap state and in the superconducting state.
