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The authors present a theoretical and numerical study of anisotropic high-temperature materials using techniques of muon spin rotation spectroscopy. Using the London theory, the method obtains information on the microscopic magnetic fields in the probe. The muon spin rotation technique is presented in some detail, especially the muon behaviour in magnetic fields. The authors then describe the superconductor and present a prescription for numerical calculations of the fields. These in turn are used to develop numerical simulations of muon stopping in superconductors. 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.