Some properties of nonlinear sigma-models in noncommutative geometry

We introduce nonlinear sigma -models in the framework of noncommutative geo metry with special emphasis on models defined on the noncommutative torus. We choose as target spaces the two point space and the circle and illustrat e some characteristic features of the corresponding sigma -models. In parti cular we construct a sigma -model instanton with topological charge equal t o 1. We also define and investigate some properties of a noncommutative ana logue of the Wess-Zumino-Witten model.