"Nanoscale objects like magnetic molecules and clusters, quantum dots, and graphene, bring us novel physical concepts. Recently, the temporal scale of the order of tens of femtoseconds (femtoscale) became available and new physical phenomena associated with this time scale, such as laser-induced electron and magnetic phase transitions, were discovered. The theoretical background for understanding this new physics is still rather poor. This temporal scale, like the spatial nanoscale is intermediate between micro- and macroworld making the standard approaches developed in micro- and macrophysics not suitable anymore. Essentially new theoretical ideas and methods are necessary for its description, especially in a combination with the spatial nanoscale. The aim of this project is to provide such a background via detailed studies of key problems, and open the way for new practical applications.Based on a combination of analytical and computational theoretical approaches (most of them were suggested by us), we plan to study systematically time-dependent many-body phenomena at the femto/nano scale. We will develop a theory of nonequilibrium magnetic interactions and spin dynamics of nanosystems and apply it to molecular magnets and clusters at metal surfaces and at graphene. We will study the physics of graphene and “artificial graphene” (array of semiconducting quantum dots) in strongly time-dependent electric fields (laser-induced ultrafast dynamics).This list covers the crucial problems in this new field (nonequilibrium spin dynamics, calculation of response functions crucial for pump-probe experiments, new physics in highly excited graphene and graphene-like systems) and the success of the project will represent a breakthrough in our understanding of the nanoworld, with very important perspectives for applications, namely, for the drastic miniaturization of basic elements and enhancing speed of basic operations in electronics."