As technology matures, communication system operation regions shift from mic- wave and millimeter ranges to sub-millimeter ranges. However, device perf- mance at very high frequencies suffers drastically from the material deficiencies. As a result, engineers and scientists are relentlessly in search for the new types of materials, and composites which will meet the device performance requirements and not present any deficiencies due to material electrical and magnetic properties. Anisotropic and gyrotropic materials are the class of the materials which are very important in the development high performance microwave devices and new types composite layered structures. As a result, it is a need to understand the wave propagation and radiation characteristics of these materials to be able to realize them in practice. This book is intended to provide engineers and scientists the required skill set to design high frequency devices using anisotropic, and gyrotropic materials by providing them the theoretical background which is blended with the real world engineering application examples. It is the author’s hope that this book will help to fill the gap in the area of applied electromagnetics for the design of microwave and millimeter wave devices using new types of materials. Each chapter in the book is designed to give the theory first on the subject and solidify it with application examples given in the last chapter. The application examples for the radiation problems are given at the end of Chap. 5 and Chap. 6 for anisotropic and gyrotropic materials, respectively, after the theory section.