(Subchapter Titles): **I. Foundations. Mathematical Preliminaries:** Analysis and Topology. Probability Theory. Algebra. **Construction of Fractal Sets:** Classical Fractal Sets. Iterated Function Systems. Recurrent Sets. Graph Directed Fractal Constructions. **Dimension Theory:** Topological Dimensions. Metric Dimensions. Probabilistic Dimensions. Dimension Results for Self-Affine Fractals. The Box Dimension of Projections. **Dynamical Systems and Dimension. II. Fractal Functions and Fractal Surfaces:** **Fractal Function Construction:** The Read-BajraktarevicOperator. Recurrent Sets as Fractal Functions. Iterative Interpolation Functions. Recurrent Fractal Functions. Hidden Variable Fractal Functions. Properties of Fractal Functions. Peano Curves. Fractal Functions of Class *C*k. **Dimension of Fractal Functions:** Dimension Calculations. Function Spaces and Dimension. **Fractal Functions and Wavelets:** Basic Wavelet Theory. Fractal Function Wavelets. **Fractal Surfaces:** Tensor Product Fractal Surfaces. Affine Fractal Surfaces in **R***n+M*. Properties of Fractal Surfaces. Fractal Surfaces of Class *Ck*. **Fractal Surfaces and Wavelets in R***n***:** Brief Review of Coxeter Groups. Fractal Functions on Foldable Figures. Interpolation on Foldable Figures. Dilation and *W* Invariant Spaces. Multiresolution Analyses. List of Symbols. Bibliography. Author Index. Subject Index.