Although there is no precise definition of a ""fractal"", it is usually understood to be a set whose smaller parts, when magnified, resemble the whole. Self-similar and self-affine sets are those for which this resemblance is precise and given by a contracting similitude or affine transformation.

Table of Contents

Chapter 1. Introduction

Chapter 2. Elements of Geometric Measure Theory

Chapter 3. General properties of self-similar sets and measures

Chapter 4. Separation properties for self-similar IFS

Chapter 5. Multifractal Analysis for self-similar measures

Chapter 6. Transversality techniques for self-similar IFS

Chapter 7. Further properties of self-similar IFS with overlaps

Chapter 8. Fourier-analytic and number-theoretic methods

Chapter 9. Elements of Ergodic Theory

Chapter 10. Self-affine sets and measures

Chapter 11. Diagonally self-affine IFS

Chapter 12. Exact dimensionality and dimension conservation

Chapter 13. Local entropy averages and projections of self-affine sets and measures

Chapter 14. Nonlinear conformal iterated functions systems

Appendix A. Some elements of Linear algebra

Appendix B. Some elements of measure theory

Appendix C. Some elements of Harmonic Analysis

Appendix D. Some facts about algebraic numbers