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.