  We present a brief introduction to the relativistic kinetic theory of gases
with emphasis on the underlying geometric and Hamiltonian structure of the
theory. Our formalism starts with a discussion on the tangent bundle of a
Lorentzian manifold of arbitrary dimension. Next, we introduce the Poincare
one-form on this bundle, from which the symplectic form and a volume form are
constructed. Then, we define an appropriate Hamiltonian on the bundle which,
together with the symplectic form yields the Liouville vector field. The
corresponding flow, when projected onto the base manifold, generates geodesic
motion. Whenever the flow is restricted to energy surfaces corresponding to a
negative value of the Hamiltonian, its projection describes a family of
future-directed timelike geodesics. A collisionless gas is described by a
distribution function on such an energy surface, satisfying the Liouville
equation. Fibre integrals of the distribution function determine the particle
current density and the stress-energy tensor. We show that the stress-energy
tensor satisfies the familiar energy conditions and that both the current and
stress-energy tensor are divergence-free.
  Our discussion also includes the generalization to charged gases, a summary
of the Einstein-Maxwell-Vlasov system in any dimensions, as well as a brief
introduction to the general relativistic Boltzmann equation for a simple gas.
