Fluid dynamics and thermodynamics are the fundamental sciences used in centrifugal compressor design and analysis. This chapter develops the fundamental fluid dynamics concepts and governing equations used throughout the book. Fluid dynamics analysis is applied in several forms for centrifugal compressors. One-dimensional analysis with empirical work input and loss models is the basis for most aerodynamic performance analysis. Detailed aerodynamic design is normally based on two- and three-dimensional inviscid flow analysis, often supported by boundary layer analysis. Computational methods based on this technology are commonly referred to as Euler codes to distinguish them from viscous flow codes; these codes are based on a mature technology. They can and should be available to any centrifugal compressor designer. Representative methods for all of these analysis techniques are covered in detail here.