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We outline a microscopic approach to the superconducting fluctuations andpairing correlations in the attractive Hubbard model above Tc, using thefunctional integral method. A crossover from BCS superconductivity to Bosecondensation of preformed pairs is studied by constructing the appropriateGinzburg-Landau functionals. The differences between the lattice and thecontinuum models are discussed. The case of quasi-two-dimensionalsuperconductors as well as the model with non-local pairing interaction arealso examined. The effects of gaussian fluctuations of the order parameter areanalyzed in the T-matrix approach, the self-consistent Hartree approach andfinally within the Ginzburg-Landau theory. Simlarities with a paramagnon theoryof itinerant-electron magnetism are pointed out.

On the Crossover from BCS Superconductivity to Bose Condensation