  These notes are devoted to the foundations of Milnor-Witt K-theory of fields
of arbitrary characteristic and without any perfectness assumptions. Extending
the fundamental work of Morel, we establish all its functorial properties as
stated in Feld's theory of Milnor-Witt modules, with a special attention about
twists. The main new result is a computation of transfers in the general (in
particular inseparable) case in terms of Grothendieck (differential) trace
maps. These notes are used as the foundation for an expository work on
Chow-Witt groups. They are built upon a series of talks given at the Spring
School ``Invariants in Algebraic Geometry'', organized by Daniele Faenzi,
Adrien Dubouloz and Ronan Terpereau.
