  Mutation is an operation on 3-manifolds containing an embedded surface of
genus 2. It is defined by cutting along the surface and regluing using the
`hyperelliptic' involution, and is known to preserve many 3-manifold
invariants. I show that mutation of a homology 3-sphere preserves its
(instanton) Floer homology, and that a related operation on 4-manifolds
preserves the Donaldson invariants. A companion article (in preparation) will
treat invariants based on the Seiberg-Witten equations.
