An introduction is provided to the mathematical tools and problems of percolation theory. A discussion of Bernoulli percolation models shows the role of graph duality and correlation inequalities in the recent determination of the critical probability in the square, triangular, and hexagonal lattice bond models. An introduction to first passage percolation concentrates on the problems of existence of optimal routes, length of optimal routes, and conditions for convergence of first passage time and reach processes.
"Percolation Theory." Ann. Probab. 10 (3) 509 - 524, August, 1982. https://doi.org/10.1214/aop/1176993764