Minimal model program for Kaehler threefolds. Lecture 1

Following recent works of A. Hoering and T. Peternell, I will describe the construction of minimal models for compact Kaehler manifolds of dimension three. In particular, I will concentrate on those fundamental difficulties which distinguish the Kaehler case from the case of a projective variety. Also I will desribe the tools from complex analytic geometry which are useful in dealing with the aforementioned problems.