The aerospace industry until mid of the 1980s has used mainly inviscid analytical, semi-empirical and numerical methods for the prediction of flows past elements of airplanes, missiles, helicopters and space planes. At that time computer power (computing capacity and storage space) for the calculation of complete viscous flow fields past complex configurations was not sufficient. On the other hand the available numerical approximation methods (stability and robustness) had not the quality of the discretisation schemes we know today. The same was true regarding the grid generation procedure. Therefore, inviscid solutions for airfoils, isolated wings and fuselages, etc., applying linear and non-linear potential equations for disturbed potentials (Panel methodpanel methods) and later Euler solutions were the options available. Today, these methods are in use as design tools for preliminary studies during the pre-design phase of future projects. Other applications are given in the frame of the establishment of aerodynamic data sets, where the inviscid approach often is sufficient. In the following several versions of the Euler equations are presented for flows with gases in the various thermodynamic states: perfect, equilibrium and chemical non-equilibrium. Quasi-linear forms of the Euler equations are derived with diagonalisation of the Jacobians to allow for the application of splitting procedures regarding numerical discretization methods. Finally, some versions of the potential equation are given.