Approximation Theory and Methods by M.J.D. Powell offers an introduction to the classical and modern techniques for approximating functions that are essential in computer calculations. The book covers polynomial approximation, focusing on both theoretical foundations and practical applications. It delves into the recent developments in piecewise polynomial methods, providing a comprehensive understanding of the subject matter. Aimed at scientists and engineers who require practical approximation methods, as well as mathematicians seeking a rigorous treatment, this text is based on lectures for third-year mathematics undergraduates at Cambridge University. With detailed analyses of various techniques and motivation throughout, it serves as an excellent resource for both theoretical insight and applied practice.