and away from the spin arrow, respectively. Considering that the huge muon spin polarization is completely outside thermal equilibrium, a dynamical relaxation towards the equilibrium unpolarized state typically shows up in the count rate, as an additional decay factor in front of the experimental asymmetry parameter, A. A magnetic field parallel to the initial muon spin direction probes the dynamical relaxation rate as a function of the additional muon Zeeman energy, without introducing additional coherent spin dynamics. This experimental arrangement is called Longitudinal Field (LF) μSR. A special case of LF μSR is Zero Field (ZF) μSR, when the external magnetic field is zero. This experimental condition is particularly important since it allows to probe any internal quasi-static (i.e. static on the muon time-scale) magnetic field of field distribution at the muon site. Internal quasi-static fields may appear spontaneously, not induced by the magnetic response of the sample to an external field They are produced by disordered nuclear magnetic moments or, more importantly, by ordered electron magnetic moments and orbital currents. Another simple type of μSR experiment is when implanted all muon spins precess coherently around the external magnetic field of modulus , perpendicular to the beam axis, causing the count unbalance to oscillate at the corresponding Larmor frequency between the same two detectors, according to Since the Larmor frequency is , with a gyromagnetic ratio Mrad(sT)−1, the frequency spectrum obtained by means of this experimental arrangement provides a direct measure of the internal magnetic field intensity distribution. The distribution produces an additional decay factor of the experimental asymmetry A. This method is usually referred to as Transverse Field (TF) μSR. A more general case is when the initial muon spin direction (coinciding with the detector axis) forms an angle with the field direction. In this case the muon spin precession describes a cone which results in both a longitudinal component, , and a transverse precessing component, , of the total asymmetry. ZF μSR experiments in the presence of a spontaneous internal field fall into this category as well. Applications Muon spin rotation and relaxation are mostly performed with positive muons. They are well suited to the study of magnetic fields at the atomic scale inside matter, such as those produced by various kinds of magnetism and/or superconductivity encountered in compounds occurring in nature or artificially produced by modern material science. The London penetration depth is one of the most