Abstract: Floer's celebrated instanton homology groups are defined for integer homology spheres, but analagous groups in Heegaard Floer and Monopole Floer homology theories are defined for all 3–manifolds; these latter groups furthermore come in four flavors, and carry extra algebraic structure. Any attempt to extend instanton homology to a larger class of 3–manifolds must be somehow equivariant — respecting a certain SO(3)–action. We explain how ideas from group cohomology and equivariant algebraic topology allow us to define four flavors of instanton homology for rational homology spheres.