Moment maps in gauge theory

Since their introduction in the context of symplectic geometry, moment maps and symplectic quotients have been generalized in many different directions. In this talk I plan to give an introduction to the notions of hyperkähler moment map and hyperkähler quotient through two examples, apparently very different, but related by the so called ADHM construction of instantons; the moduli space of instantons and a space of complex matrices arising from monads.