  In this thesis, I present a non-perturbative approach to the single-band
attractive Hubard model which is an extension of previous work by Vilk and
Tremblay on the repulsive model. Exact results are derived in the general
context of functional derivative approaches to many-body theories. The first
step of the approximation is based on a local field type ansatz. All physical
quantities can be expressed as a function of double-occupancy (in addition to
temperature and filling). Double-occupancy is determined without adjustable
parameter by imposing the Pauli principle and a crucial sum-rule, making the
first step of the approximation Two-Particle Self-Consistent. The final
expression for the self-energy is obtained by calculating the low-frequency
part of the exact expression with the two-particle correlation, Green function
and renormalized vertex obtained in the first step of the approximation. The
Mermin-Wagner theorem in two dimensions is automatically satisfied. Application
of this non-perturbative many-body approach to the intermediate coupling regime
shows quantitative agreement with quantum Monte Carlo calculations. Both
approaches predict the existence of a pseudogap in the single-particle spectral
weight. I present some physical properties, such as correlation lengths,
superfluid density, and characteristic pair fluctuation energy, to highlight
the origin of the pseudogap in the weak to intermediate coupling regime. These
results suggest that two-dimensional systems that are described by a symmetry
group larger than SO(2) could have a larger region of pseudogap behavior.
High-temperature superconductors may belong to that category of systems.
