This book aims at providing a handy explanation of the notions behind the self-similar sets called 'fractals' and 'chaotic dynamical systems'. The authors emphasize the beautiful relationship between fractal functions (such as Weierstrass') and chaotic dynamical systems; these nowhere-differentiable 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.