This book presents the theory and application of new methods of image compression based on self-transformations of an image. These methods lead to a representation of an image as a fractal, an object with detail at all scales. Very practical and completely up-to-date, this book will serve as a useful reference for those working in image processing and encoding and as a great introduction for those unfamiliar with fractals. The book begins with an elementary introduction to the concept of fractal image compression and contains a rigorous description of all the relevant mathemtics of the subjects.