Nonlinear optical studies of periodic dielectric structures have blossomed in the past two decades. New fabrication techniques are producing fiber grating and multidimensional photonic crystals in materials where the refractive index can be varied by light pulses and beams. Gap solitons that can propagate at any velocity from zero to the speed of light and spatial solitons that prevent the diffractive spread of light in waveguide arrays are two examples of the new phenomena described in this book. Microstructured optical fibers allow control of the guided mode dispersion for broadband light generation and new soliton phenomena. Many new materials and structures are being developed that will impact new optical devices with applications in optical communications and optical data processing. All the above topics are addressed in detail in this book.