This book is the first monograph ever on complex-valued neural networks, which lends itself to graduate and undergraduate courses in electrical engineering, informatics, control engineering, mechanics, robotics, bioengineering, and other relevant fields. It is useful for those beginning their studies, for instance, adaptive signal processing for highly functional sensing and imaging, control in unknown and changing environment, brainlike information processing, robotics inspired by human neural systems, and interdisciplinary studies to realize comfortable society. It is also helpful to those who carry out research and development regarding new products and services at companies. The author wrote this book hoping in particular that it provides the readers with meaningful hints to make good use of neural networks in fully practical applications. The book emphasizes basic ideas and ways of thinking. Why do we need to consider neural networks that deal with complex numbers? What advantages do the complex-valued neural networks have? What is the origin of the advantages? In what areas do they develop principal applications? This book answers these questions by describing details and examples, which will inspire the readers with new ideas.