The motto of connectivity and superconductivity is that the solutions of the Ginzburg Landau equations are qualitatively in?uenced by the topology of the boundaries. Special attention is given to the zero set, the set of the positions (usually known as quantum vortices ) where the order parameter vanishes. The paradigm of connectivity and superconductivity is the Little Parks e?ect, discussed in most textbooks on superconductivity. This volume is intended to serve as a reference book for graduate students and researchers in physics or mathematics interested in superconductivity, or in the...