Geometric invariant theory studies an action of a group "G" on an algebraic variety (or scheme) "X" and provides techniques for forming the 'quotient' of "X" by "G" as a scheme with reasonable properties. One motivation was to construct moduli spaces in algebraic geometry as quotients of schemes parametrizing marked objects. In the 1970s and 1980s the theory developed interactions with symplectic geometry and equivariant topology, and was used to construct moduli spaces of objects in differential geometry, such as instantons and monopoles.