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I would like to recommend to you the following lecture notes by V.P. Nair. These lecture notes contain a very concise chapter about twistors, their relation to massless wave equations and their use in the construction of Yang-Mills amplitudes. The importance of this work to me is that, here, Nair connects these two applications to another (may be less famous) application of twistors in the theory of quantization on geometrically nontrivial manifolds (such as the quantization problem of a particle moving on the two sphere in the presence of a monople).