Deep study of the Nahm equations was carried out by Nigel Hitchin and Simon Donaldson. Conceptually, the equations arise in the process of infinite-dimensional hyperkähler reduction. They can also be viewed as a dimensional reduction of the anti-self-dual Yang-Mills equations (Donaldson 1984). Among their many applications we can mention: Hitchin's construction of monopoles, where this approach is critical for establishing nonsingularity of monopole solutions ; Donaldson's description of the moduli space of monopoles ; and the existence of hyperkähler structure on coadjoint orbits of complex semisimple Lie groups, proved by (Kronheimer 1990), (Biquard 1996), and (Kovalev 1996).