  These lecture notes provide the material for a short introductory course on
effective equations for classical particle systems. They concern the basic
equations in kinetic theory, written by Boltzmann and Landau, describing
rarefied gases and weakly interacting plasmas respectively. These equations can
be derived formally, under suitable scaling limits, taking classical particle
systems as a starting point. A rigorous proof of this limiting procedure is
difficult and still largely open. We discuss some mathematical problems arising
in this context.
