For each thermodynamic system, it is possible to determine a relation between energy, entropy, and the work parameters (the volume only in the case of simple systems) that is called the Fundamental Relation of the system. We start first with closed systems with no chemical reactions for which the Equilibrium State Postulate determines, in general, the number of degrees of freedom and then it is generalized to open systems with variable chemical composition. The Fundamental Relation describes the set of all stable and metastable equilibrium states that the system can reach and the geometrical properties of the surface described by it determines the conditions of stability of equilibrium states. It can be represented in various forms according to the external constraints. The representations commonly used, in addition to that of Energy and of Entropy, are the Free Energy, the Enthalpy, and the Gibbs Potential and the general properties of isothermal, isobaric and isochoric transformations are discussed. The definition of the chemical potential is given and its physical meaning as the thermodynamic potential responsible of phase equilibria is shown.