  This work assembles some basic theoretical elements on thermal equilibrium,
stability conditions, and fluctuation theory in self-gravitating systems
illustrated with a few examples. Thermodynamics deals with states that have
settled down after sufficient time has gone by. Time dependent phenomena are
beyond the scope of this paper. While thermodynamics is firmly rooted in
statistical physics, equilibrium configurations, stability criteria and the
destabilizing effect of fluctuations are all expressed in terms of
thermodynamic functions. The work is not a review paper but a pedagogical
introduction which may interest theoreticians in astronomy and astrophysicists.
It contains sufficient mathematical details for the reader to redo all
calculations. References are only to seminal works or readable reviews. (Except
in the ultimate sub-section.) Delicate mathematical problems are mentioned but
are not discussed in detail.
