  Slave-spin mean-field theory, a light and accurate technique to model
electronic correlations in Fermi-liquid phases of multi-orbital materials, is
pedagogically exposed in this chapter, with a focus on its recent successful
application to the physics of Iron-based superconductors. Beside introducing
electronic correlations and recalling the Fermi-liquid phenomenology, the
manuscript accompanies the step-by-step explanation of the slave-spin technique
with a set of useful complements providing analytical insight into Mott and
Hund's physics, which are at the heart of the physics of strongly correlated
materials. Some original research material is also exposed, such as the
Hund-induced shrinking of the Hubbard bands flanking the gap of the half-filled
Mott insulator, and the low-energy description of the "orbital-decoupling"
mechanism.
