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This pedagogical review of galaxy cluster simulations is based on three lectures given at the 2008 Enrico Fermi Summer School entitled "Astrophysics of Galaxy Clusters". It covers the standard cosmological framework, growth of perturbations in the linear regime, analytic models for nonlinear perturbation growth, statistics of galaxy cluster populations, virial scaling relations, overview of numerical methods, simulating gas in galaxy clusters, basic results on adiabatic clusters (Santa Barbara cluster comparison project), effect of additional physics, recent progress in galaxy clustering modeling (Galcons, turbulence, AGN jets, cluster-wide B-fields), simulating statistical samples and lightcones, and simulated SZE surveys.
preprint / 2010