  Yang-Mills instantons on ALE gravitational instantons were constructed by
Kronheimer and Nakajima in terms of matrices satisfying algebraic equations.
These were conveniently organized into a quiver. We construct generic
Yang-Mills instantons on ALF gravitational instantons. Our data are formulated
in terms of matrix-valued functions of a single variable, that are in turn
organized into a bow. We introduce the general notion of a bow, its
representation, its associated data and moduli space of solutions. For a
judiciously chosen bow the Nahm transform maps any bow solution to an instanton
on an ALF space. We demonstrate that this map respects all complex structures
on the moduli spaces, so it is likely to be an isometry, and use this fact to
study the asymptotics of the moduli spaces of instantons on ALF spaces.
