In this chapter we will establish the relation of the Lagrange parameters to the temperature, chemical potential and the pressure. Furthermore, thermodynamical potentials are introduced for the different ensembles, that are functions of the natural variables as well as their total differentials. The latter lead to various Maxwell relations between thermodynamic quantities. We will formulate (and prove) the main laws of thermodynamics and discuss in particular the specific heat and the thermal expansion coefficient. It will be shown, that the classical ideal gas violates in particular the 3rd law of thermodynamics. Finally, we will discuss different changes of state and compute the efficiency coefficient for the Carnot cycle and the Otto engine.