  Various topics at the interface between condensed matter physics and the
physics of ultra-cold fermionic atoms in optical lattices are discussed. The
lectures start with basic considerations on energy scales, and on the regimes
in which a description by an effective Hubbard model is valid. Qualitative
ideas about the Mott transition are then presented, both for bosons and
fermions, as well as mean-field theories of this phenomenon. Antiferromagnetism
of the fermionic Hubbard model at half-filling is briefly reviewed. The
possibility that interaction effects facilitate adiabatic cooling is discussed,
and the importance of using entropy as a thermometer is emphasized. Geometrical
frustration of the lattice, by suppressing spin long-range order, helps
revealing genuine Mott physics and exploring unconventional quantum magnetism.
The importance of measurement techniques to probe quasiparticle excitations in
cold fermionic systems is emphasized, and a recent proposal based on stimulated
Raman scattering briefly reviewed. The unconventional nature of these
excitations in cuprate superconductors is emphasized.
