This book gives an elementary introduction to a classical area of mathemat- ics - approximation theory - in a way that naturally leads to the modern field of wavelets. The main thread throughout the book is the idea of ap- proximating "complicated expressions" with "simpler expressions," and how this plays a decisive role in many areas of modern mathematics and its applications. One of the main goals of the presentation is to make it clear to the reader that mathematics is a subject in a state of continuous evolution. This fact is usually difficult to explain to students at or near their...