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. The second half treats recent topics such as volume minimizations related to Sasaki-Einstein metrics and some symplectic geometry including deformation quantization.

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