AB-initio excited states calculations for semiconductor materials: From bulk to low dimensional systems

First-principles ground-state calculations on different kind of materials are currently carried out within density functional theory. On the other hand a correct description of the electronic excitations, which are at the origin of many experimental spectra, requires more refined theories. In this paper we summarize the main equations of the theoretical many-body approach used to describe electronic and optical properties of real materials. Some examples of excited state calculations in bulk and low dimensional semiconducting systems are given.