This book gives a mathematically rigorous and self-contained presentation of the hp method for Computational Fluid Dynamics (CFD). The presentation begins with an introduction of the fundamental concepts related to both h and p methods using simple one-dimensional model PDEs and continues with the more complex PDEs governig multidimensional incompressible and compressible flows of practical interest. In addition to the clear and complete presentation of the mathematical theory, sufficient guidelines and implementation details are given throughout the presentation of the material. This book is very helpful to both newcomers in the field of CFD as well as experienced practitioners who wish to apply hp refinement methods in CFD.