Twistors and Aspects of Integrability of self-dual SYM Theory

With the help of the Penrose-Ward transform, which relates certain holomorphic vector bundles over the supertwistor space to the equations of motion of self-dual SYM theory in four dimensions, we construct hidden infinite-dimensional symmetries of the theory. We also present a new and shorter proof (cf. hep-th/0412163) of the relation between certain deformation algebras and hidden symmetry algebras. This article is based on a talk given by the author at the Workshop on Supersymmetries and Quantum Symmetries 2005 at the BLTP in Dubna, Russia.