  Linear stability and the non-modal transient energy growth in compressible
plane Couette flow are investigated for two prototype mean flows: (a) the {\it
uniform shear} flow with constant viscosity, and (b) the {\it non-uniform
shear} flow with {\it stratified} viscosity. Both mean flows are linearly
unstable for a range of supersonic Mach numbers ($M$). For a given $M$, the
critical Reynolds number ($Re$) is significantly smaller for the uniform shear
flow than its non-uniform shear counterpart. An analysis of perturbation energy
reveals that the instability is primarily caused by an excess transfer of
energy from mean-flow to perturbations. It is shown that the energy-transfer
from mean-flow occurs close to the moving top-wall for ``mode I'' instability,
whereas it occurs in the bulk of the flow domain for ``mode II''. For the
non-modal analysis, it is shown that the maximum amplification of perturbation
energy, $G_{\max}$, is significantly larger for the uniform shear case compared
to its non-uniform counterpart. For $\alpha=0$, the linear stability operator
can be partitioned into ${\cal L}\sim \bar{\cal L} + Re^2{\cal L}_p$, and the
$Re$-dependent operator ${\cal L}_p$ is shown to have a negligibly small
contribution to perturbation energy which is responsible for the validity of
the well-known quadratic-scaling law in uniform shear flow: $G(t/{\it Re}) \sim
{\it Re}^2$. A reduced inviscid model has been shown to capture all salient
features of transient energy growth of full viscous problem. For both modal and
non-modal instability, it is shown that the {\it viscosity-stratification} of
the underlying mean flow would lead to a delayed transition in compressible
Couette flow.
