  These notes summarize a series of works related to the numerical
approximation of plasma fluid problems. We construct so-called
'Asymptotic-Preserving' schemes which are valid for a large range of values
(from very small to order unity) of the dimensionless parameters that appear in
plasma fluid models. Specifically, we are interested in two parameters, the
scaled Debye length which quantifies how close to quasi-neutrality the plasma
is, and the scaled cyclotron period, which is inversely proportional to the
magnetic field strength. We will largely focus on the ideas, in order to enable
the reader to apply these concepts to other situations.
