Near-field optical microscopy allows the nondestructive examination of surfaces with a spatial resolution far below the diffraction limit of Abbe. In fact, the resolution of this kind of microscope is not at all dependent on the wavelength, but is typically in the range of 10 to 100 nanometers. On this scale, many materials are anisotropic, even though they might appear isotropic on the macroscopic length scale. In the present work, the previously never studied interaction between a scattering-type near-field probe and an anisotropic sample is examined theoretically as well as experimentally. In the theoretical part of the work, the analytical dipole model, which is well known for isotropic samples, is extended to anisotropic samples. On isotropic samples one observes an optical contrast between different materials, whereas on anisotropic samples one expects an additional contrast between areas with different orientations of the same dielectric tensor. The calculations show that this anisotropy contrast is strong enough to be observed if the sample is excited close to a polariton resonance. The experimental setup allows the optical examination in the visible and in the infrared wavelength regimes. For the latter, a free-electron laser was used as a precisely tunable light source for resonant excitation. The basic atomic force microscope provides a unique combination of different scanning probe microscopy methods that are indispensable in order to avoid artifacts in the measurement of the near-field signal and the resulting anisotropy contrast. Basic studies of the anisotropy contrast were performed on the ferroelectric single crystals barium titanate and lithium niobate. On lithium niobate, we examined the spectral dependence of the near-field signal close to the phonon resonance of the sample as well as its dependence on the tip-sample distance, the polarization of the incident light, and the orientation of the sample. On barium titanate, analogous measurements were performed and, additionally, areas with different types of domains were imaged and the near-field optical contrast due to the anisotropy of the sample was directly measured. The experimental results of the work agree with the theoretical predictions. A near-field optical contrast due to the anisotropy of the sample can be measured and allows areas with different orientations of the dielectric tensor to be distinguished optically. The contrast results from variations of the dielectric tensor components both parallel and perpendicular to the sample surface. The presented method allows the optical examination of anisotropies of a sample with ultrahigh resolution, and promises applications in many fields of research, such as materials science, information technology, biology, and nanooptics.