My research concerns the control of finite- and infinite-dimensional quantum systems, via mathematical methods. Approximation techniques are usually applied for studying the whole system, in order to reduce its complexity and be able to analyze it via algebraic methods. Important examples of systems which can be tackled with these techniques are molecules and their rotational dynamics. Another relevant technique, beside approximations, is given by the adiabatic control of open quantum systems. An example here is the STIRAP process. There, I am interested in the spectral properties of the adiabatic evolution of a control system, seen as a perturbation of a closed dynamic.