The authors present a theoretical and numerical study of anisotropic high-temperature materials with muon spin rotation spectroscopy. They obtain information on the microscopic magnetic fields in the probe. The muon spin rotation technique, muon behaviour in magnetic fields, the superconductor, and a prescription for numerical calculations of the fields are presented. These are used to develop numerical simulations of muon stopping in superconductors, and the results are presented graphically. This is the first text to combine muon spectroscopy with Fourier methods in scientific computing. The book addresses researchers including those working in industry.