These lecture notes are based on the theory of experimental design for courses given by Valerii Fedorov at a number of places, most recently at the University of Minnesota, the Vienna of University, and the University of Economics and Business Administra­ tion in Vienna. It was Peter Hackl's idea to publish these lecture notes and he took the lead in preparing and developing the text. The work continued longer than we expected, and we realized that a few thousand miles distance remains a serious hurdle even in the age of Internet and many electronic gadgets. While we mainly target graduate students in statistics, the book demands only a moderate background in calculus, matrix algebra and statistics. These are, to our knowledge, provided by almost any school in business and economics, natural sciences, or engineering. Therefore, we hope that the material may be easily understood by a relatively broad readership. The book does not try to teach recipes for the construction of experimental de­ signs. It rather aims at creating some understanding - and interest - in the problems and basic ideas of the theory of experimental design. Over the years, quite a number of books have been published on that subject with a varying degree of specialization. This book is organized in four chapters that layout in a rather compact form all.