  A comprehensive review of the equations of general relativity in the
quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is made.
Our main interest concerns its applications to the analysis of the perturbation
of standard cosmology in the Friedman-Lema\^itre-Robertson-Walker framework.
The major achievement of the QM scheme is its use of completely gauge
independent quantities. We shall see that in the QM-scheme we deal directly
with observable quantities. This reveals its advantage over the old method
introduced by Lifshitz et al that deals with perturbation in the standard
Einstein framework. For completeness, we compare the QM-scheme to the
gauge-independent method of Bardeen, a procedure consisting on particular
choices of the perturbed variables as a combination of gauge dependent
quantities.
