This book is intended for those wishing to acquire a working knowledge of orthogonal transforms in the area of digital signal processing. The authors hope that their introduction will enhance the opportunities for interdiscipli- nary work in this field. The book consists of ten chapters. The first seven chapters are devoted to the study of the background, motivation and development of orthogonal transforms, the prerequisites for which are a basic knowledge of Fourier series transform (e.g., via a course in differential equations) and matrix al- gebra. The last three chapters are relatively specialized in that they are di- rected toward certain applications of orthogonal transforms in digital signal processing. As such, a knowlegde of discrete probability theory is an essential additional prerequisite. A basic knowledge of communication theory would be helpful, although not essential. Much of the material presented here has evolved from graduate level courses offered by the Departments of Electrical Engineering at Kansas State University and the University of Texas at Arlington, during the past five years. With advanced graduate students, all the material was covered in one semester. In the case of first year graduate students, the material in the first seven chapters was covered in one semester. This was followed by a prob- lems project-oriented course directed toward specific applications, using the material in the last three chapters as a basis.