(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.