We study the emergence of transport processes such as diffusion, viscosity, or heat conduction from the microscopic motion of the
atoms and molecules composing matter. We aim at bridging the gap separating the micro- from the macroscale, thanks to appropriate
mechanistic and stochastic descriptions holding at mesocopic scales and allowing one to derive exact expressions for the transport
coefficients and other kinetic properties. We have an ongoing project on heat conduction in a class of many-particle billiards,
one of the main challenges in modern nonequilibrium statistical mechanics. The existence of heat conductivity is demonstrated, the
associated coefficient is calculated by analytical methods in appropriate limits and the thermodynamic entropy production is
deduced from the hydrodynamic modes.  Methods of kinetic theory such as Vlasov equation are also developed for models of microplasmas
and self-gravitating systems.