Of all the systems in statistical mechanics on which exact calculations have been performed, the two-dimensional Ising model is not only the most thoroughly investigated; it is also the richest and most profound. In 1925, Ising introduced the statistical system which now bears his name and studied some of its properties in one dimension. Although the generalization of Ising's system to higher dimensions was immediately obvious, it was not until 1941 that a quantitative statement about the phase transition in the two-dimensional case was made when Kramers and Wannier and also Montroll computed the Curie (or critical) temperature. However, the most remarkable development was made in 1944 when Onsager was able to compute the thermodynamic properties of the two-dimensional lattice in the absence of a magnetic field.