This comprehensive and popular textbook makes fractal geometry accessible to final-year undergraduate math or physics majors, while also serving as a reference for research mathematicians or scientists. This up-to-date edition covers introductory multifractal theory, random fractals, and modern applications in finance and science. "Falconer's book is excellent in many respects and the reviewer strongly recommends it. May every university library own a copy, or three! And if you're a student reading this, go check it out today!." (Mathematical Association of America, 11 June 2014)