[en] We derive a precise mathematical connection between the strong-coupling regime of the Abelian lattice gauge theory in four dimensions and a lattice model of a superconductor. This connection relates the quark confinement of the lattice gauge theory to magnetic flux tubes in the superconductor, along lines conjectured earlier by Mandelstam and't Hooft. We apply this relation to the study of the behavior of physical quantities in the vicinity of the transition of the gauge theory to its quark-confining phase. In the course of our arguments, we develop an analogous connection between models describing a superconductor and a ferromagnet in three dimensions; this analysis reveals a new second-order phase transition in a superconductor which may be interpreted as a Gell-Mann-Low eigenvalue in (2+1) -dimensional scalar QED