Double and triple diagrams of metal systems condition are considered. The method of isothermal and polythermal sections construction and analysis of phase transformations in various alloys is described, the structure is given. The theoretical foundations of thermodynamics are considered in its application to the study of phase equilibria. Using the method of geometric thermodynamics, an analysis of double state diagrams was carried out. In the analysis of three-component state diagrams with double and triple intermediate phases with several four-phase ionvariant reactions, structural diagrams of phase equilibria were used.