In recent years, there has been a rapid expansion in the field of nonlinear optics as weIl as in the field of neural computing. Up to date, no one would doubt that nonlinear optics is one of the most promising fields of realizing large neural network models due to their inherent parallelism, the use of the speed of light and their ability to process two-dimensional data arrays without carriers or transformation bottlenecks. This is the reason why so many of the interesting applications of nonlinear optics - associative memories, Hopfield networks and self-organized nets - are realized in an all optical way using nonlinear optical processing elements. Both areas attracting people from a wide variety of disciplines and judged by the proliferation of published papers, conferences, international collaborations and enterprises, more people than ever before are now inΒ volved in research and applications in these two fields. These people all bring a different background to the area, and one of the aims of this book is to provide a common ground from which new development can grow. Another aim is to explain the basic concepts of neural computation as weIl as its nonlinear optical realizations to an interested audiΒ ence. Therefore, the book is about the whole field of optical neural network applications, covering all the major approaches and their important results. Especially, it its an inΒ troduction that develops the concepts and ideas from their simple basics through their formulation into powerful experimental neural net systems.