With the coming of the computer age, fractals have emerged to play a significant role in art images, scientific application and mathematical analysis. The Beauty of Fractals is in part an exploration of the nature of fractals, including examples which appear in art, and in part a close look at famous classical fractals and their close relatives. The final essay examines the relationship between fractals and differential equations. The essays that appear in The Beauty of Fractals contain perspectives different enough to give the reader an appreciation of the breadth of the subject. The essays are self-contained and expository, and are intended to be accessible to a broad audience that includes advanced undergraduate students and teachers at both university and secondary-school level. The book is also a useful complement to the material on fractals which can be found in textbooks.