This article addresses two issues on thermodynamics, namely, the calculation of solubility lines and the calculation of the activity of various components. It discusses alloying elements in terms of their influence on the activity of carbon. The article describes the desulfurization and deoxidation of cast iron and steel. It illustrates the thermodynamics of the iron-carbon system and the iron-silicon system. The article examines solubility and saturation degrees of carbon in multicomponent iron-carbon systems. One of the main applications of the thermodynamics of the iron-carbon system is the calculation of structure-composition correlations. The article concludes with information on the structural diagrams for cast iron: the Maurer diagram and the Laplanche diagram.