*Result*: Finite-Dimensional Percolation

*In this chapter we apply the scaling theories developed in the one-dimensional system and the infinite-dimensional system to systems of finite dimensions. The lowest dimension with an interesting behavior is two dimensions. Here, we introduce effective ways to measure the cluster number density $$n(s,p)$$ n ( s , p ) in two dimension. We develop the scaling theory for $$n(s,p)$$ n ( s , p ) and demonstrate how to use data-collapse plots as an efficient method to measure the critical exponents. We also demonstrate how we can use the scaling theory for $$n(s,p)$$ n ( s , p ) to derive expressions for the density of the spanning cluster, P , and the average cluster size, S . Finally, we demonstrate how the scaling theory provides scaling relations, that is, relations between exponents, and bounds for the values of the critical exponents.*