This chapter highlights some of the fundamental concepts from thermodynamics that are essential to the aerodynamic design and analysis of axial-flow compressors. These concepts provide the basis for defining and evaluating the energy transfer processes and for modeling the state properties of the working fluid. Unlike the centrifugal compressor, axial-flow compressors are most often applied to rather ideal working fluids, the most common being air. But the application of axial-flow compressors to non-ideal working fluids is becoming more common. Consequently, a basic description of non-ideal gas modeling is included. This description is sufficient for application of the techniques, but is less detailed than this author's previous description for centrifugal compressors (Aungier, 2000). Readers interested in more detail are referred to that earlier reference or to Aungier (1995, 1998).