A study of the Euler equation on the basis of one-dimensional velocity triangles provides insights into energy transfer in compressors, emphasising the importance of the centrifugal effect in the impeller, the diffusion of the flow and the degree of reaction. An introduction to thermodynamics is given leading to the steady flow energy equation (SFEE), which is the first law of thermodynamics applied to a fixed region with steady flow passing through it. The SFEE is used to account for the changes in fluid properties along the flow path and shows that the bookkeeping of the energy transfer needs to be carried out using the total enthalpy or the rothalpy. The study of compressors needs to consider the efficiency of processes concerned. The Gibbs equation, a form of the second law of thermodynamics, provides a rigorous way to do this through the thermodynamic state variable known as entropy. In the context of energy transfer, the entropy production characterises the lost work in the machine due to dissipation losses. Isentropic and polytropic compression processes are explained. The important concept of the aerodynamic work and the value of a polytropic analysis are considered.