Local ADHM construction and holomorphic local vector bundles on the twistor space

Local ADHM theory has been discussed; after making some general remarks about Penrose transform and methods of monad, we construct holomorphic vector bundles on the neighbourhood of a projective line in the twister space. By inverse Ward transformation this corresponds to local solution space of self-dual Yang-Mills equation. In the final section we discuss some possible applications of this theorem.