The apparent differences in the statements of the phase rule for the two sets of variables commonly used, namely, temperature, pressure, and mole fractions on the one hand and temperature, pressure, and chemical potentials on the other are resolved by developing a framework in which the phase rule may be stated and analyzed in terms of a whole class of variable sets. The framework is restricted to the case where all the components are present in all the phases. Central to the framework is the notion, due to Gibbs, of a fundamental relation for homogeneous states and the associated general equation cast in terms of intensive and specific variables. The significance of the Gibbs-Duhem equations within the context of the phase rule is brought out. The lead provided by Gibbs in his approach to the phase rule is utilized to carry out a local analysis of the equations that result from the criteria of equilibrium for the two sets of variables referred to above. The central role played by the general equations is brought out. The scope of the phase rule is widened by identifying particular sets of variables that would be suitable for uniquely defining the equilibrium state of a multiphase mixture.