The kinetic theory of gases is a most fruitful field for mathematical research. This is evident from the multiplicity of mathematical methods used, the originality of the questions posed and the large number of hitherto unsolved fundamental problems. For example, the question of existence and uniqueness of solutions of various non-linear kinetic equations is still a wide open one. Simplified model equations and various approximations therefore assume considerable significance for the understanding of problem structure and for the solution of practical problems.