  Assuming the existence of a fundamental thermodynamic relation, the classical
thermodynamics of a black hole with mass and angular momentum is given. New
definitions of response functions and $TdS$ equations are introduced and
mathematical analogous of the Euler equation and Gibbs-Duhem relation are
founded. Thermodynamic stability is studied from concavity conditions,
resulting in an unstable equilibrium at all the domain except for a region of
local stable equilibrium. Maxwell relations are written, allowing to build the
thermodynamic squares. Our results shown an interesting analogy between
thermodynamics of gravitational and magnetic systems.
