Yang-Mills connections with L^2 anti-self-dual curvature, called instantons, play significant role in geometry and in physics. Atiyah, Drinfeld, Hitchin, and Manin discovered a construction of all instantons on Euclidean four-space in terms of algebraic data organized into a quiver. This ADHM construction can be viewed as a version of a nonlinear Fourier transform. It was generalized by Nahm to instantons on R^3xS^1 as well as to monopoles. We begin with a review of these two constructions and then describe instantons on other hyperhahler spaces. In these lectures we focus on instantons on multi-Taub-NUT space and give their complete construction in terms of a generalization of a quiver, called a bow.