  We outline a microscopic approach to the superconducting fluctuations and
pairing correlations in the attractive Hubbard model above Tc, using the
functional integral method. A crossover from BCS superconductivity to Bose
condensation of preformed pairs is studied by constructing the appropriate
Ginzburg-Landau functionals. The differences between the lattice and the
continuum models are discussed. The case of quasi-two-dimensional
superconductors as well as the model with non-local pairing interaction are
also examined. The effects of gaussian fluctuations of the order parameter are
analyzed in the T-matrix approach, the self-consistent Hartree approach and
finally within the Ginzburg-Landau theory. Simlarities with a paramagnon theory
of itinerant-electron magnetism are pointed out.
