This book aims at providing a handy explanation of the notions behind the selfsimilar sets called "fractals" and "chaotic dynamical systems". The authors emphasize the beautiful relationship between fractal functions (such as Weierstrass's) and chaotic dynamical systems; these nowheredifferentiable functions are generating functions of chaotic dynamical systems. These functions are shown to be in a sense unique solutions of certain boundary problems. The last chapter of the book treats harmonic functions on fractal sets. Readership Undergraduate students, graduate students, and research mathematicians interested in global analysis and analysis on manifolds. Reviews "Pleasant reading ... encourages the reader who is interested in fractals and their properties to pursue the study of the subject."  Mathematical Reviews "The book is a good introduction to the topic. Interesting applications are presented."  European Mathematical Society Newsletter "If you must pick a book, on which an instructor can base a course, then the material must be built up systematically  both making connections to fundamental and elementary ideas in analysis  and, at the same time, it must reach some highpoints in the subject. This lovely little book does that ... it has great exercises."  Palle Jorgensen Table of Contents  The fundamentals of fractals
 Selfsimilar sets
 An alternative computation for differentiation
 In quest of fractal analysis
 Recommended reading
 Index
