Hans-Otto Georgii, Olle Haggstrom, Christian Maes The random geometry of equilibrium phases (1496K, Postscript) ABSTRACT. We present a review on the random geometry of equilibrium phases. Percolation methods are used to study the nature of equilibrium statistical mechanical systems. Important themes are random-cluster representations, uniqueness and exponential mixing from non-percolation, and phase transitions from percolation.