  This tutorial provides an overview of the local description of polarization
for nonparaxial light, for which all Cartesian components of the electric field
are significant. The polarization of light at each point is characterized by a
$3$ component vector in the case of full polarization or by a $3\times3$
polarization matrix for partial polarization. Standard concepts for paraxial
polarization like the degree of polarization, the Stokes parameters and the
Poincar\'e sphere then have generalizations for nonparaxial light that are
either not unique or not trivial. This work aims to clarify some of these
discrepancies, present some new concepts, and provide a framework that
highlights the similarities and differences with the description for the
paraxial regimes. Particular emphasis is placed on geometric interpretations.
