The development of wavelets is fairly recent in applied mathematics, but wavelets have already had a remarkable impact. A lot of people are now applying wavelets to a lot of situations, and all seem to report favorable results. What is it about wavelets that make them so popular? What is it that makes them so useful? This prologue will present an overview in broad strokes (using descriptions and analogies in lieu of mathematical formulas). It is intended to be a brief preview of topics to be covered in more detail in the chapters. It might be useful for the reader to refer back to the prologue from time to time, to prevent the possibility of getting bogged down in mathematical detail to the extent that the big picture is lost. The prologue describes the forest; the trees are the subjects of the chapters.