This book is the first comprehensive textbook on the optical properties of photonic crystals. It deals not only with the properties of the radiation modes inside the crystals but also with their peculiar optical response to external fields. A general theory of linear and nonlinear optical response is given in a clear and detailed fashion using Green's function method. The symmetry of the eigenmodes is treated systematically using group theory to show how it affects the optical properties of photonic crystals. Important recent developments such as the enhancement of stimulated emissions, second harmonic generation, quadrature-phase squeezing, and low-threshold lasing are also treated in detail and made understandable. Numerical methods are also emphasized. Thus this book provides both introductory knowledge for graduate and undergraduate students and also important ideas for researchers in this field.