My objective is the development of theoretical and numerical approaches to describe new kind of spectroscopy, based on non-linear optics, using ab initio methods such as Density Functional Theory. Second harmonic generation constitutes a way to explore materials in a non-destructive way, but it is difficult to interpret, and theory is very much needed. We have developed theory and a computer code to calculate second harmonic generation in periodic systems . These developments give access to problems such as Electric Field Induced SHG, non-linear optics of surfaces and interfaces , and the search for new materials for non-linear optics .