  This paper addresses the linear propagation of an electron wave in a
collisionless, inhomogeneous, nonstationary and anisotropic plasma. The plasma
is characterized by its distribution function, $f_H$, at zero order in the wave
amplitude. This distribution function, from which are derived all the
hydrodynamical quantities, may be chosen arbitrarily, provided that it solves
Vlasov equation. Then, from the linearized version of the electrons equation of
motion, and from Gauss law, is derived an envelope equation for the wave
amplitude, assumed to evolve over time and space scales much larger than the
oscillation periods of the wave. The envelope equation may be cast into an
equation for the the wave action, derived from Whitham's variational principle,
that demonstrates the action decay due to Landau damping. Moreover, the Landau
damping rate is derived at first order in the variations of the wave number and
frequency. As briefly discussed, this paper generalizes numerous previous works
on the subject, provides a theoretical basis for heuristic arguments regarding
the action decay, and also addresses the propagation of an externally driven
wave.
