(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 Ck. 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 Rn+M. Properties of Fractal Surfaces. Fractal Surfaces of Class Ck. Fractal Surfaces and Wavelets in Rn: 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.