Werner Ballmann : Lectures on Kähler Manifolds

These notes are based on lectures the author held at the University of Bonn and the Erwin-Schrodinger-Institute in Vienna. The aim is to give a thorough introduction to the theory of Kahler manifolds with special emphasis on the differential geometric side of Kahler geometry. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture.