Percolation theory was founded by Broadbent and Hammersley [1957] almost half a century ago; by now, thousands of papers and many books have been devoted to the subject. The original aim was to open up to mathematical analysis the study of random physical processes such as the flow of a fluid through a disordered porous medium. These bona fide problems in applied mathematics have attracted the attention of many physicists as well as pure mathematicians, and have led to the accumulation of much experimental and heuristic evidence for many remarkable phenomena. Mathematically, the subject has turned out to be much more difficult than might have been expected, with several deep results proved and many more conjectured.

The first spectacular mathematical result in percolation theory was proved by Kesten: in 1980 he complemented Harris's 1960 lower bound on the critical probability for bond percolation on the square lattice, and so proved that this critical probability is 1/2. To present this result, and numerous related results, Kesten [1982] published the first monograph devoted to the mathematical theory of percolation, concentrating on discrete two-dimensional percolation. A little later, Chayes and Chayes [1986b] came close to publishing the next book on the topic when they wrote an elegant and very long review article on percolation theory understood in a much broader sense.

For nearly two decades, Grimmett's 1989 book (with a second edition published in 1999) has been the standard reference for much of the basic theory of percolation on lattices.