This chapter is devoted to the aerodynamics and thermodynamics of four shaft engines: internal combustion (IC), turboprop, turboshaft, and propfan engines (Figure 6.1). The tree presented in Figure 6.1 illustrates air-breathing engines, which are so named as they need only air for combustion while carrying appropriate fuels [1]. Consequently, these propulsion systems stop working outside the atmosphere of Earth. The aim when designing shaft-based engines is to achieve higher power (or thrust) and less weight (using advanced composite materials), thus achieving a high thrust-to-weight ratio. Other goals are to achieve a smaller frontal area, reduced chemical emissions (CO2, SO x , and NO x ), low-level exterior noise, better cooling characteristics, and lower fuel consumption. Moreover, during production, it can be built using green processes and materials.