Scattering theory covers a large spectrum of scientific and technological applications such as non destructive control, radars, sonar, geophysical exploration, remote sensing, medical imaging, under-water acoustics, seismology, biological pattern recognition and special techniques in medical diagnostics. In most of the above cases the assumption that the material is isotropic is inadequate. Therefore, in order to conform to reality, we have to accept that the space is anisotropic, i.e., its properties depend on the direction. Although the anisotropic property was already known, since Green's era, only a few publications have appeared, due to the mathematical complexity related with the anisotropic property. It was during the last years that more references considered the anisotropic scattering, while most of them regarded only anisotropic scatterers.The thesis examines the problem of scalar field anisotropic scattering for the general case, where not only the scatterer but also the propagation space are anisotropic and they do not have the same characteristics.