Provides a modern introduction to Kählerian geometry and Hodge theory. It starts with basic material on complex variables, complex manifolds, holomorphic vector... » 

Provides a modern introduction to Kählerian geometry and Hodge theory. It starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves, and cohomology theory. The book ends with a treatment of the deformations of the complex structure, Gauss-Manin connection, and variations of Hodge structure, and th study of algebraic cycles. «