  The subject matter of this paper concerns the derivation of the finite Larmor
radius approximation, when collisions are taken into account. Several studies
are performed, corresponding to different collision kernels. The main
motivation consists in computing the gyroaverage of the Fokker-Planck-Landau
operator, which plays a major role in plasma physics. We show that the new
collision operator enjoys the usual physical properties; the averaged kernel
balances the mass, momentum, kinetic energy and dissipates the entropy.
