Kinetic Theories and the Boltzmann Equation : Lectures given at the 1st 1981 Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held at Montecatini Italy June 10 – 18 1981 Time dependent linear transport theory An introduction to the nonlinear boltzmann vlasov equation The Boltzmann equation and its properties Preliminary results on the non existence of solutions for a half space boltzmann collision model with three degrees of freedom The space homogeneous Boltzmann equation for molecular forces of infinite range The cauchy problem for the Boltzmann equation. A survey of recent results Boltzmann hierarchy and boltzmann equation A nonlinear half space problem in the kinetic theory of gases.