Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. The book provides a significant contribution to material already published about the beautiful mathematical objects drawn by computers using recursive or iterative algorithms. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. There are changes throughout the text in this updated edition, taking into account developments in the subject matter since 1990. Sections have been rewritten and are now clearer and more focused. The book also contains many good illustrations of fractals, including 16 color plates.