Techniques for generating orthogonal polynomials numerically have appeared only recently, within the last 30 years. These techniques and related applications, all supported by MATLAB programs, are here described and presented in a unique format consisting of copious exercises and solutions, designed by the author to stimulate reader participation. Important computational problems in the physical sciences are also included as models for readers to then solve their own problems. Having been described as a 'very valuable addition to the literature on orthogonal polynomials', this book will benefit mathematicians, computer scientists, and all types of engineers and scientists, as well as students.