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These lecture notes provide the material for a short introductory course oneffective equations for classical particle systems. They concern the basicequations in kinetic theory, written by Boltzmann and Landau, describingrarefied gases and weakly interacting plasmas respectively. These equations canbe derived formally, under suitable scaling limits, taking classical particlesystems as a starting point. A rigorous proof of this limiting procedure isdifficult and still largely open. We discuss some mathematical problems arisingin this context.

A brief introduction to the scaling limits and effective equations in kinetic theory