Moduli Space of Self-Dual Gauge Fields, Holomorphic Bundles and Cohomology Sets

We discuss the twistor correspondence between complex vector bundles over a self-dual four-dimensional manifold and holomorphic bundles over its twistor space and describe the moduli space of self-dual Yang-Mills fields in terms of Cech and Dolbeault cohomology sets. The cohomological description provides the geometric interpretation of symmetries of the self-dual Yang-Mills equations.