This handbook has been compiled with the aim of providing a clear, organised, and accessible collection of fundamental equations, assumptions, and modelling frameworks that underpin the study of thermodynamics and fluid dynamics for both perfect gases and non-ideal fluids. The document systematically tidies up and clarifies many behaviours, derivations, and relationships that are frequently encountered in research and industrial practice but are often scattered across various textbooks and publications. Covering topics from basic assumptions and equations of state to compressible flows, turbulence, and turbomachinery, it serves as a concise yet comprehensive reference for students, researchers, and practising engineers alike.