Ultracold Fermi gases: The BEC-BCS crossover

We give an introduction to the present state of research in the field of ultracold atomic Fermi gases. Of particular interest is the search for (BCS) superfluidity in these systems. The existence of Feshbach resonance have made these systems especially flexible, allowing to control at will the strength and the sign of the effective interaction. In particular it has allowed an experimental realization of the Bose-Einstein Condensation (BEC)-BCS crossover, allowing to display on one side a Bose condensate of molecules and on the other side a BCS superfluid produced by Cooper pairs. Then we focus more specifically to the shift of the molecular threshold, produced by Pauli exclusion in these degenerate gas. We discuss also briefly collective modes corresponding to oscillations of the gas in the harmonic trap in which it is confined.