"The project will explore many-body physics in emergent quantum Hall effect systems (graphitic layers and surface states of topological insulators) and in layered metals of transition metal dichalcogenides using magneto-optical spectroscopy - unconventional for this purpose, but uniquely applicable to these unconventional systems. Studying the inter Landau level excitations (with Raman scattering techniques) in graphene and its bilayer we will test the basic principles of the role of electron-electron interactions in the regime of the quantum Hall effect. Employing high sensitivity microwave absorption methods, we will attempt to solve one of the most controversial issues in the physics of graphene: the nature of the low temperature ground state of the graphene bilayer. The magneto-optical response (in the far-infrared range) of three dimensional topological insulators will be investigated with the aim of demonstrating a new (half odd-integer) quantum Hall effect of their surface states and possible new exotic ground states of single-cone Dirac fermions. Finally, with a fresh experimental approach (cyclotron resonance absorption on NbSe2 and TaS2 and their thin layers) we will shed new light on one of the most intriguing phenomena in strongly correlated systems: competition between an insulating behaviour (charge density wave state in our case) and the ideal-conductor, superconductivity phase."