The aim of this textbook is to provide the reader with an elementary introduction to fractal geometry and chaotic dynamics: subjects which have attracted immense interest throughout the scientific and engineering disciplines. The book may be used in part or as a whole to form an introductory course in either or both subject areas. A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. Plenty of problems are provided to test understanding. In addition, advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas. The book can be used as a text for undergraduate courses or for self-study. Students, teachers and professionals in science, engineering, economics, medicine and social science requiring an introduction to fractals and chaos should find the book useful. Parts of the book are suitable as a readable introduction for the general reader with some basic mathematics.