"This is the first systematic study of best approximation theory in inner product spaces and, in particular, in Hilbert space. Geometric considerations play a prominent role in developing and understanding the theory. The only prerequisites for reading the book are some knowledge of advanced calculus and linear algebra. Throughout the book, examples and applications have been interspersed with the theory. Each chapter concludes with numerous exercises and a section in which the author puts the results of that chapter into a historical perspective. The book is based on lecture notes for a graduate course on best approximation that the author has taught for over twenty-five years."--BOOK JACKET.