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We study the lattice analogues of the Wess-Zumino-Witten (WZW) and Toda conformal field theories. We describe discrete versions of the Drinfel'd-Sokolov reduction and the Sugawara construction for the WZW model, and show how to formulate a perturbation theory in the chiral sector. We describe the spaces of integrals of motion of the perturbed theories. We interpret the perturbed WZW model in terms...