The thermodynamic observables of the classical one– and two–dimensional ferromagnetic and antiferromagnetic Ising models on a square lattice are simulated, especially at the phase transitions (if applicable) using the classical Monte Carlo algorithm of Metropolis. Finite size effects and the influence of an external magnetic field are described. The critical temperature of the 2d ferromagnetic Ising model is obtained using finite size scaling. 1. Statistical mechanics -- a short review 2. Monte Carlo simulation 3. Selected results A. Source code of MC integrators B Implementation of the Ising models Bibliography List of Figures