  We develop a unified description, via the Boltzmann equation, of damping of
gravitational waves by matter, incorporating collisions. We identify two
physically distinct damping mechanisms -- collisional and Landau damping. We
first consider damping in flat spacetime, and then generalize the results to
allow for cosmological expansion. In the first regime, maximal collisional
damping of a gravitational wave, independent of the details of the collisions
in the matter is, as we show, significant only when its wavelength is
comparable to the size of the horizon. Thus damping by intergalactic or
interstellar matter for all but primordial gravitational radiation can be
neglected. Although collisions in matter lead to a shear viscosity, they also
act to erase anisotropic stresses, thus suppressing the damping of
gravitational waves. Damping of primordial gravitational waves remains
possible. We generalize Weinberg's calculation of gravitational wave damping,
now including collisions and particles of finite mass, and interpret the
collisionless limit in terms of Landau damping. While Landau damping of
gravitational waves cannot occur in flat spacetime, the expansion of the
universe allows such damping by spreading the frequency of a gravitational wave
of given wavevector.
