The book begins with a thorough discussion of the equations of fluid mechanics with emphasis on their mathematical properties. Techniques of discretization are discussed next, followed by a short section on transformations and grids. The first part of the book closes with sections on source and vortex panel methods for incompressible flows and a section on explicit methods for compressible flows. The second part contains four self-contained chapters on more advanced material: boundary layer methods, implicit time-marching methods, finite volume methods and finite element methods.