This report presents an account of the course "Nonlinear Spectroscopy of Solids: Advances and Applications" held in Erice, Italy, from June 16 to 30, 1993. This meeting was organized by the International School of Atomic and Molecular Spectroscopy of the "Ettore Majorana" Centre for Scientific Culture. The purpose of this course was to present and discuss physical models, mathematical formalisms, experimental techniques, and applications relevant to the subject of nonlinear spectroscopy of solid state materials. The universal availability and application of lasers in spectroscopy has led to the widespread observation of nonlinear effects in the spectroscopy of materials. Nonlinear spectroscopy encompasses many physical phenomena which have their origin in the monochromaticity, spectral brightness, coherence, power density and tunability of laser sources. Conventional spectroscopy assumes a linear dependence between the applied electromagnetic field and the induced polarization of atoms and molecules. The validity of this assumption rests on the fact that even the most powerful conventional sources of light produce a light intensity which is not strong enough to equalize the rate of stimulated emission and that of the experimentally observed decay. A different situation may arise when laser light sources are used, particularly pulsed lasers. The use of such light sources can make the probability of induced emission comparable to, or even greater than, the probability of the observed decay; in such cases the nonlinearity of the response of the system is revealed by the experimental data and new properties, not detectable by conventional spectroscopy, will emerge.