TITLE: Some references for potential theory and complex differential geometry
QUESTION [8 upvotes]: I am looking for references on two distinct (though related) topics.

Potential theory : 
I read some time ago the book of Ransford (Potential Theory in the complex plane). It was great (intuitive and relatively elementary) but now insufficient for my purposes. In particular I'd like a book that works on a more general setting (manifolds, more than 1 variable). Anyone has a good one ?
Complex geometry
I realize that is a vast topic. I already have a background in differential geometry, a bit of Riemann surfaces. What I need to learn about is stuff like : $\overline{\partial}$ and $dd^c$ operators, quadratic differentials on a complex manifold, residues of complex forms... I know this is not very precise but hey, if I knew exactly what I were looking for I wouldn't need to ask...

REPLY [4 votes]: The standard textbook now on the subject is Complex Geometry:An Introduction by Daniel Huybrechts.  It has relatively little in the way of prerequisites: A good course in complex analysis, basic differential topology and algebra. It looks excellent and doesn't try to do too much so it becomes overwhelming-this is a difficult subject after all.
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