This monograph is devoted to the theory of the design of optimal experiments. It introduces new ideas of the author that are an integral part of mathematical foundations of factorial experiments. The book presents a new concept of factorial models and addresses the issues of construction of effective plans for them. It contains numerous examples and a catalogue of factorial designs. The monograph will be useful to practitioners involved in experiments in various fields of industry and science, and it will be useful to researchers. This book will also be a valuable addition to core curriculum for senior and graduate students studying the design of experiments.