The global objective of the project is to develop a theoretical framework for the first-principles description of the macroscopic electromagnetic response of solids with a full and accurate account of the spatial dispersion and memory effects. The new scheme will be applied to study two fundamental properties of extended systems: the natural optical activity and the magnetoelectric effect in crystals of technological relevance, such as multiferroics and topological insulators. We should state that at present there is no theory able to model the frequency-dependent response of extended systems with the full account of spatial dispersion. The response of these systems to static fields has been widely studied in recent years and among others has given rise to the development of what is known as the modern theory of polarisation. The present project aims at the extension of those theories to the time-domain and will certainly have a big impact in the fields of condensed matter, material science, nano- and bioscience. The outcome of the project would be delivered to the whole scientific community as part of the Octopus project that aims to have a fully versatile free (GNU license) code able to describe the time-dependent electron-ion dynamics of finite and extended systems to arbitrary intense and time-dependent electromagnetic perturbations.The solution of the challenging theoretical problem addressed by the project requires combination of the expertise of the host in modeling electronic properties of matter and the strong background of the researcher in theoretical physics, materials science and computational methods. The know-how of the researcher in multi-level modeling and close collaboration with industry will help to raise the level of the host group in these areas. The project will be a seed to the long-term collaboration between the host group and the present group of the researcher in Russia.