The starting PhD student or the non-specialist, typically an experimentalist in material science who whish to go throught this fascinating physics is quickly faced to a "gap" in the litterature on the subject, between the elementary textbooks and documents for specialists, as well as the dispersion of interesting sources. This document is a synthesis and a compilation of these different textes, in order to make them more avalaible and hence to help who want to go throught this subject. It follows an increasing complexity and review the different concepts settled to understand this physics. One will find a short reminder on Fermi liquids, then a discussion around the Hubbard Hamiltonian followed by a discussion around real materials. The Metal-Insulator Transition "à la" Hubbard is then discussed, followed by the Gutzwiller-Brinkan-Rice and his reformulation in terms of slave bosons. At the end, the Dynamical Mean Field Theory is analysed to discuss to his application on real materials.
