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This book is devoted entirely to the development of the least quadratic problems and their applications. The textbook is an outgrowth of the lecture notes that the author has used in a graduate course for several years in the Department of Mathematics at the University of Wisconsin, Madison. This book has also been complemented by the author's association with the control system group at Honeywell Inc., Minneapolis, MN. This cooperation has yielded a unique and extremely informative textbook that contains a rich body of analysis, design, and/or numerical algorithms that have immediate useful applications in the real control-engineering world. In the preface the author says that his aim in this textbook is to expose a body of materials to an audience, “scientifically literate, but without the extensive preparation in engineering and innocent of most mathematics beyond elementary analysis and linear algebra.” Bridging this gap is one of the unique and excellent features of this textbook.