Fractal Examples.- Metric Topology.- Topological Dimension.- Self-Similarity.- Measure Theory.- Fractal Dimension.- Additional Topics.
What exactly is a Fractal?
From the reviews of the second edition:
"As a non-specialist, I found this book very helpful. It gave me a better understanding of the nature of fractals, and of the technical issues involved in the theory. I think it will be valuable as a textbook for undergraduate students in mathematics, and also for researchers wanting to learn fractal geometry from scratch. The material is well-organized and the proofs are clear; the abundance of examples is an asset for a book on measure theory and topology." (Fabio Mainardi, MathDL, February, 2008)
"This is the second edition of a well-known textbook in the field ... . The book may serve as a textbook for a one-semester (advanced) undergraduate course in mathematics. ... the book is also suitable for readers interested in theoretical fractal geometry coming from other disciplines (e.g. physics, computer sciences) with a basic knowledge of mathematics. The presentation of the material is appealing ... and the style is clear and motivating. ... the book will remain as a standard reference in the field." (Jose-Manuel Rey, Zentralblatt MATH, Vol. 1152, 2009)