The aim of this textbook is to provide the reader with an elementary introduction to fractal geometry and chaotic dynamics. These are subjects which have attracted immense interest throughout the whole range of numerate disciplines, including science, engineering, medicine, economics, and social science, to name but a few. The book may be used in part or as a whole to form an introductory course in either or both of the subject areas. The text is very much 'figure driven' as I believe that illustrations are extremely effective in conveying the concepts required for comprehension of the subject matter of the book. In addition, undue mathematical rigour is often avoided within the text in order to provide a concise treatment of specific concepts and speed the reader through the subject areas.