Composite materials present unique challenges to the traditional roles of material scientists and engineers. A composite material can be custom tailored to have specific properties that will meet special requirements. However, a composite material has added dimensions of complexity with respect to engineering analyses which involve complicated mathematical models. These models may be constructed using tensor notation which lends itself well in affording a means of formulating compact mathematical models and yet contain a large amount of information. This book has been arranged consistently to present the mechanics of composite materials using Cartesian tensors as a shorthand. It introduces students to the fundamental concepts of the mechanical behavior of composite materials. In addition, it provides a solid foundation for further study and research. This book is based on a one-semester graduate course that I give. It is intented as a graduate level textbook. However, it may be used by students, researchers and practicing engineers for reference.