The first two editions of this book have been very well received by the com munity, but so many revisions ofthe Maple system have occurred since then that simply reprinting the out-of-stock book would not do anymore. A ma jor revision of the book was inevitable, too. The wording "major revision" must be taken seriously because I not only corrected typographical errors, rephrased text fragments, and updated many examples, but I also rewrote complete chapters and added new material. In particular, the chapter on differential equations now discusses Liesymmetry methods, partial differen tial...

The nine review articles in this book give a fairly complete survey of the applications of fractals to astronomical and astrophysical problems. The book is self-contained and written with the particular aim of teaching graduate students how to apply fractal geometry to new problems. After ageneral introduction to the basic concepts, applications are given to astrophysical dynamical systems, to strange attractors of stellar pulsations, to the solar granular pattern, and to both the large-scale structure of the universe - a central theme of the book - and to astronomical data analysis.