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The study of the magnetic response of Josephson junction networks can be useful in outlining the behaviour of existing superconducting electronic devices, in conceiving new types of magnetic sensors, and in describing the low-field magnetic properties of granular superconductors. In the present work a wide introduction to Josephson junction networks is provided. The Josephson equations are introduced by means of Ohta's semi-classical model and a simple description of the magnetic response of multiply connected superconductors is given. The analysis of the magnetic response of Josephson junction networks is gradually built up from simple interferometers to three-dimensional lattices of superconducting devices. The analytic description of these systems may be applied when fabricating ultrasensitive vectorial magnetic field sensors and interpreting the low-field magnetic properties of superconducting granular systems.