The interaction of light with matter, in particular metals, is one of the classical areas of physical studies, and has contributed tremendously to our present understanding of physics. Light has been used successfully to investigate the electronic, magnetic and atomic structure of metal surfaces, as well as thin films, multi-layers, and interfaces. Such optical studies represent a non-destructive technique for materials characterization. The study of magnetism is of particular interest, not only for basic research, but also in view of a variety of applications like storage of information and magnetic recording. For many years the linear Kerr effect, typically exhibiting in metals Kerr rotations of less than one degree, has been used and developed as a successful tool for solid state physics research and applications. Only recently nonlinear optical effects in metals and in particular nonlinear magneto-optical effects have become an intensive area of studies. Due to the high interface sensitivity of nonlinear magneto-optics in contrast to linear magneto-optics, such studies lead to a new tool of investigating electronic stucture and magnetism at metallic interfaces, in thin films and multilayers. The high sensitivity of nonlinear optics and in particular the related, strikingly large Kerr rotations have been a remarkable experimental observation and an impressive example that Maxwell's equations still offer surprises. While future work on electronic and atomic structural phase transitions, on lateral and in-depth resolution of film structure, magnetic contrasts, domain structures, anti-ferromagnetism, or magnetic anisotropy effects will reveal the full potential of second harmonic light generation as a new tool of interface and film research, this book will give a comprehensive introduction to the state of the art in the subject, and will lay the ground for further developments.