Theoretical Models for Photonic Crystals.- Models for Infinite Crystals.- Models for Finite Crystals.- Quasi-Crystals and Archimedean Tilings.- Specific Features of Metallic Structures.- Optical Properties of Photonic Crystals.- Control of Electromagnetic Waves.- Refractive Properties of Photonic Crystals and Metamaterials.- Confinement of Light in Zero-Dimensional Microcavities.- Nonlinear Optics with Photonic Crystals.- Fabrication, Characterization and Applications of Photonic Bandgap Structures.- Planar Integrated Optics.- Microsources.- Photonic Crystal Fibres.- Three-Dimensional Structures in Optics.- Microwave and Terahertz Antennas and Circuits.- Conclusion and Perspectives.