  Magnetic helicity is a fundamental quantity of magnetohydrodynamics that
carries topological information about the magnetic field. By `topological
information', we usually refer to the linkage of magnetic field lines. For
domains that are not simply connected, however, helicity also depends on the
topology of the domain. In this paper, we expand the standard definition of
magnetic helicity in simply connected domains to multiply connected domains in
$\mathbb{R}^3$ of arbitrary topology. We also discuss how using the classic
Biot-Savart operator simplifies the expression for helicity and how domain
topology affects the physical interpretation of helicity.
