Introduction to complex manifolds / John M. Lee.

Includes bibliographical references and index.

The basics -- Complex submanifolds -- Holomorphic vector bundles -- The Dolbeault complex -- Sheaves -- Sheaf cohomology -- Connections -- Hermitian and Kähler manifolds -- Hodge theory -- The Kodaira embedding theorem.

This graduate-level textbook provides a comprehensive introduction to the theory of complex manifolds from the perspective of differential geometry. Beginning with the foundations of smooth and complex manifolds, the book develops the essential concepts, techniques, and structures used in modern complex geometry, including holomorphic maps, complex submanifolds, vector bundles, Dolbeault cohomology, sheaf theory, Hermitian and Kähler geometry, Hodge theory, and the Kodaira embedding theorem. Emphasizing intuition together with mathematical rigor, the author explains how analytic, topological, and geometric ideas interact in the study of complex manifolds. Numerous examples, exercises, and detailed proofs make the text suitable for graduate students and researchers seeking an accessible yet advanced treatment of complex geometry and its applications in differential geometry, algebraic geometry, topology, and mathematical physics.