  These lectures give an introduction to the theory of holographic
superconductors. These are superconductors that have a dual gravitational
description using gauge/gravity duality. After introducing a suitable
gravitational theory, we discuss its properties in various regimes: the probe
limit, the effects of backreaction, the zero temperature limit, and the
addition of magnetic fields. Using the gauge/gravity dictionary, these
properties reproduce many of the standard features of superconductors. Some
familiarity with gauge/gravity duality is assumed. A list of open problems is
included at the end.

High Energy Physics - Theory;General Relativity and Quantum Cosmology