µSR owes its user comminity mostly to physicists and material scientists involved in magnetism, but superconductivity is the second field of election. The reason is quite apparent: muons can map the internal magnetic field distribution, which is very drastically modified in a superconductor.
The field-temperature phase diagram of superconductors may be very complicated and a few fundamental properties and quantities of the superconducting state are directly accessible from the field distribution inside the material.
This type of application historically follows that of NMR, which has a very similar capability.
However nuclei with spin larger than suffer from the complications of additional quadrupolar interactions and often the time scale of dynamical relaxations interferes with the detection of the mere static field distribution, whereas the measure with muons is at first glance quite straightforward.
For a start we shall describe very simplified models: the London model of a superconductor, the Pippard corrections due to the finite mean free path of electrons, a hint at the Ginzburg-Landau equations, and a description of how to get the field distribution in the simplest cases with examples of matlab programs.