Topics in Kähler geometry
The first half is an introduction to Kähler Geometry focusing on the problem of finding a Kähler metric of constant scalar curvature. We start with foundations of connections and curvature, and then review old and new existence results of Kähler-Einstein metrics and known obstructions such as K-stability. We will treat also Sasaki-Einstein metrics, and other generalizations of Einstein metrics. Toric manifolds will also be treated as a particular case.
 A. Futaki : Kähler-Einstein metrics and integral invariants.
Springer Lecture Notes, vol. 1314, 1988.
 G. Székelyhidi : An introduction to extremal Kähler metrics, AMS, 2010.
 P. Gauduchon : Calabi's extremal Kähler metrics: An elementary introduction.
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