This article introduces percolation theory, which is a mathematical model that is useful in the description of many physical phenomena. It is also a prime example of a model with a sharp phase transition. Firstly, it explains the theoretical background and defines the relevant parameters, quantities, and phenomena, including the spontaneous appearance of self-similarity and fractals at the percolation transition. The latter is explained using the techniques of renormalization. Finally, it presents some applications of percolation theory, and in detail illustrates its use in describing the spontaneous magnetization of a random, dilute spin ?$\frac{1}{2}$? Ising model of magnetism in various dimensions.

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