In this chapter, physical and chemical transformations are considered as a route from a less stable to a more stable equilibrium state. Initially, only physical transformations are considered describing the first and second thermodynamic laws and thermodynamic properties like internal energy, enthalpy, and entropy. Next, thermodynamic equilibrium in chemically reacting systems is considered, defining “chemical potential” as the driving force for reactions and examining in detail chemical equilibrium conditions. Equilibrium reactions between gases at different pressures are considered and the fugacity concept to describe the behavior of real gases is introduced. Different methods for determining pressure and fugacity are described. Equilibrium reactions between reactants in the liquid phase are also considered, introducing the concept of activity. Different methods for determining activity coefficients are described. Several examples of equilibrium calculations are reported. MATLAB code associated with these examples is available online. Finally, vapor–liquid equilibrium is examined in detail considering its applications in a flash-unit and a tray-distillation column.