This chapter introduces the extensive state variable known as entropy. Most of the theory of thermodynamics concerns entropy in some way. Its most important attribute is that it can only increase in irreversible processes. The chapter discusses some of the properties of entropy and its consequences. A method involving the notion of entropy, the very existence of which depends on the second law of thermodynamics, will doubtless seem to many far-fetched, and may repel beginners as obscure and difficult of comprehension. Focusing on the state of equilibrium rather than on processes is called Gibbsian thermodynamics. The stability requirements allow people to establish the direction of processes as systems come to equilibrium. The process can be systematized using the properties of Jacobian determinants, or simply Jacobians. The word entropy was intentionally chosen by Rudolf Clausius to be close to the word energy.