  The linear MHD Kelvin-Helmholtz instability (KHI) in an anisotropic plasma
concerning the direction of an external magnetic field is examined in detail.
For this purpose, the MHD equations are used to describe the motion of plasma
as a fluid, which is derived from 16 moments of Boltzmann-Vlasov kinetic
equations for collisionless plasma. In addition, the heat flux along the
magnetic field is taken into account. The growing rates of KHI are calculated
as functions of the anisotropic plasma properties for a shear flow along the
magnetic field at supersonic velocities. On the other hand, the
quasi-transverse propagation of surface waves between flows with varying
velocities is thoroughly examined for both zero-width and finite-width
transition layers. In contrast to the tangential discontinuity, it is proved
that the limiting breadth of the transition layer constrains the KHI excitation
as the wavenumber grows. The instability under investigation could be one of
the main ways of dissipation of large-scale low-frequency Alf\'en wave
turbulence existing in the solar wind plasma.
