This book contains an exposition of the theory and methods of optimum experimental design. It is aimed at giving an exact and systematic mathematical presentation of a topic which is sufficiently evolved to be considered a self-contained part of mathematical statistics. The book will be useful as an introductory text for researchers in the field, as textbook for students of statistics, and as a theoretical background for users of optimum design in experimental research: physics, chemistry, geodesy, building and electrical engineering, etc.