The thermodynamic theory of capillary phenomena is considered. The comparative analysis of Gibbs, Hansen's and Guggenheim's methods is presented. The Gibbs and Hansen's reference systems are described. An alternative geometrical interpretation of Gibbs method is developed. The adsorption equation is obtained in Hansen's representation. A symmetrized form of the adsorption equation has been derived and the relationship between Gibbs and Hansen's surface excesses established. Frumkin's interpretation of surface excesses is discussed. A description is given of the specific volume and entropy of an interface formation in a multicomponent system. The difficulties encountered in the interpretation of Hansen's method are explained. Hansen's method has been generalized for the curved surface of an arbitrary shape. The Gibbs phase rule for immiscible electrolyte solutions is considered. Methods of choosing the independent system variables that are most suitable for the electrocapillarity theory are analyzed. The thermodynamic theory of electrocapillarity phenomena at the interface between two immiscible electrolyte solutions (ITIES) is presented. A generalized electrocapillary equation for polarizable and reversible interfaces is derived using Hansen's method. The Gibbs equation for electrolytic systems is obtained both in ion concentrations and in variables corresponding to concentrations of neutral ion combinations. The relationship between the ion concentrations in the system and the EMF of the circuit consisting of immiscible electrolyte solutions with terminals made of identical metals is discussed. The formulas for the thermodynamic and the free charge of the interface between two immiscible electrolyte solutions are analysed. The cases of perfectly, ideally polarizable and reversible (nonpolarizable) interfaces are considered. Relationships between thermodynamic charges in different sets of variables are obtained.