This textbook is intended for a graduate-level course and assumes familiarity with basic concepts from matrix theory, linear algebra, and linear system theory. Six appendices at the end of the book provide the reader with enough background and review material in all these areas. This original work offers the most comprehensive and up-to-date treatment of the important subject of optimal linear estimation, which is encountered in many areas of engineering such as communications, control, and signal processing, and also in several other fields, e.g., econometrics and statistics. The book not only highlights the most significant contributions to this field during the 20th century, including the works of Wiener and Kalman, but it does so in an original and novel manner that paves the way for further developments in the new millennium. This book contains a large collection of problems that complement the text and are an important part of it, in addition to numerous sections that offer interesting historical accounts and insights. The book also includes several results that appear in print for the first time.