Abstract This chapter presents the bases of exergy and obtains expressions for its calculation. The meaning of the First Law and the Energy Conservation equations are developed, for closed and open systems. Next, Second Law is presented, reviewing its classical formulation and the entropy concept. The meaning of the distinct quality of the different forms of energy and the concept of exergy are afterwards presented. A precise definition of the reference environment and the difficulties encountered in this regard are shown. The expression for calculating the exergy of a heat flux is given, as well as the exergy associated with the internal energy and several examples are developed. A detailed exergetic study of thermal radiation is then made. For open systems, the expression of the maximum work associated with a flow is derived. The general exergy balance in an open system is then considered. Next, different ways of defining performance are given. The chapter ends with an analysis of the mechanisms of irreversibilities.