Book excerpt: Percolation theory provides a mathematical framework for the study of random physical processes such as flow through disordered porous media. It spans applications in the physical sciences and beyond natural phenomena. Double in size, this second edition provides an up-to-date account of these applications. After reviewing the theory, the book covers a range of applications and variations. Well known in the field, the author presents examples in phase transitions, semiconductors, geology, astrophysics, network modeling, and the social sciences.