  This paper gives a concise, mathematically rigorous description of
phenomenological equilibrium thermodynamics for single-phase systems in the
absence of chemical reactions and external forces.
  The present approach is similar to that of Callen, who introduces in his
well-known thermodynamics book the basic concepts by means of a few postulates
from which everything else follows. His setting is modified to match the more
fundamental approach based on statistical mechanics. Thermodynamic stability is
derived from kinematical properties of states outside equilibrium by rigorous
mathematical arguments, superseding Callen's informal arguments that depend on
a dynamical assumption close to equilibrium.
  From the formulas provided, it is an easy step to go to various examples and
applications discussed in standard textbooks such as Callen or Reichl. A full
discussion of global equilibrium would also involve the equilibrium treatment
of multiple phases and chemical reactions. Since their discussion offers no new
aspects compared with traditional textbook treatments, they are not treated
here.
