In a Functionally Graded Material (FGM), the composition and structure gradually change over volume, resulting in corresponding changes in the properties of the material. By applying the many possibilities inherent in the FGM concept, it is anticipated that materials will be improved and new functions for them created. A comprehensive description of design, modelling, processing, and evaluation of FGMs as well as their applications is covered in this book. In the simplest FGMs, two different material ingredients change gradually from one to the other. Discontinuous changes such as a stepwise gradation of the material ingredients can also be considered an FGM. The most familiar FGM is compositionally graded from a refractory ceramic to a metal. It can incorporate incompatible functions such as the heat, wear, and oxidation resistance of ceramics and the high toughness, high strength, machinability and bonding capability of metals without severe internal thermal stress. Pores are also important material ingredients for FGMs. The gradual increase of pore distribution from the interior to the surface can impart many properties such as mechanical shock resistance, thermal insulation, catalytic efficiency and relaxation of thermal stress. Even if the gradation of material ingredients is limited to a specific location in the material such as the interface, a joint, or a surface, it can be considered a functionally graded material because it includes the FGM concept. Although the FGM concept can be extended to materials with functions that are designed to change gradually over time or with changes in environmental conditions (e.g. a drug delivery system), these time-dependent functions are produced by tailoring the spatial distribution of the material ingredients. The production of multiple or new functions with graded structures rather than the graded material itself is the basis of the FGM concept reflected in this book.