Some books which migh be helpful

Topology

• Luke G., Mishchenko A., Vector bundles and their applications
• Anatoly Fomenko, Dmitry Fuchs Homotopic topology
• Michael Atiyah K-Theory
• John Milnor, James D. Stasheff Characteristic classes

• Arthur L. Besse Einstein Manifolds
• Andrei Moroianu, Lectures on Kahler Geometry
• Jean-Pierre Demailly, Complex Analytic and Differential Geometry
• Liviu Ornea, Misha Verbitsky, Principles of Locally Conformally Kahler Geometry,

• Geometrie riemannienne en dimension 4 (Seminaire Arthur Besse 1978/79).
• Daniel Huybrechts Lectures on K3 Surfaces
• A. Beauville, Complex algebraic surfaces

Misha Verbitsky, K3 surfaces IMPA