(Dedicated to the memory of Israel Moiseevich Gelfand.)
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 is formulated in terms of matrix-valued functions of a single variable, that are organized into a bow. We introduce the general notion of a bow, its representation, its associated data and moduli space of solutions. 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.