This book is  about percolation theory and its various applications, which occur mostly in physics and chemistry. The book is self-sufficient in that it contains chapters on elementary probability theory and Monte Carlo simulation. Most attention is paid to the relationship between the geometrical and physical properties of systems in the vicinity of their percolation thresholds. The theory is applied to examples of impurity semiconductors and doped ferromagnetics, which demonstrate its universality. Although written for students at high schools, the book is very good reading for college students and will satisfy the curiosity of a physicist for whom this will be a first encounter with percolation theory.The book was translated from the Russian by V. I. Kisin and was first published by Mir in 1986.