The research on extreme waves is a very active field of research in physical and human sciences, such as hydrodynamics and oceanography, geology, meteorology, biological systems, financial markets, and medical sciences. In the last ten years, extreme or rogue waves have also been observed in nonlinear optics, particularly in the context of nonlinear pulse propagation in optical fibers. Experiments and theory have rapidly progressed on nonlinear optical extreme waves, showing that guided wave nonlinear optics and fiber lasers provide a relatively simple, accessible and controllable test bed for the observations and accurate statistical studies of extreme wave phenomena that obey the same universal rules, which apply to a large ensemble of different physical systems. In spite of substantial and rapid scientific progress in this area, which led to a number important cross-fertilizations between optics and hydrodynamics rogue and extreme wave phenomena (such as the dynamics of modulation instabilities and Peregrine solitions), there is no comprehensive treatment of optical extreme wave research. With introductory material to make the subject area accessible to non-specialists such as graduate and PhD students, and researchers working in other areas where extreme waves are relevant, this book features contributions by prominent scientists in this emerging field.