Please give me some advice on references of complex geometry

Question

Recently I am reading complex geometry and preparing for my complex geometry exam. Our lectures book is so disorder and brief that I have to consult Wikipedia and math-overflow. I need some materials of complex geometry such as almost complex manifolds, Kähler manifolds, complex and holomorphic vector bundles, Hodge theory, Chern classes and sheaf theory. So can you recommend some complex geometry lectures or books to me?

Any help will be greatly appreciated!

Thanks in advance!

Answer 1

I do not know a complete book of complex geometry as you wish; therefore I print here a list of books with a brief overview on their.

1. Ballmann W. - Lectures on Kähler Manifolds. A nice text devoted to Kähler manifolds.
2. Huybrechts D. - Complex Geometry. An Introduction. A very complete text on subject, with two appendicies: one on Hodge theory and the other one on sheaves cohomology.
3. Kobayashi S. - Differential Geometry of Complex Vector Bundles. A clear and complete text on holomorphic vector bundles.
4. Voisin C. - Hodge Theory and Complex Algebraic Geometry, Volumes I and II. "The texts of Hodge theory."