Eigenmodes of Photonic Crystals -- Symmetry of Eigenmodes -- Transmission Spectra -- Optical Response of Photonic Crystals -- Defect Modes in Photonic Crystals -- Band Calculation with Frequency-Dependent Dielectric Constants -- Photonic Crystal Slabs -- Low-Threshold Lasing Due to Group-Velocity Anomaly -- Quantum Optics in Photonic Crystals -- Superfluorescence -- Epilogue.This 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 developed in a clear and detailed fashion using the 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 emission, 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 an introduction for graduate and undergraduate students and also key information for researchers in this field. This second edition has been updated and includes a new chapter on superfluorescence.