This projects aims to explore physics of the new class of materials: atomically thin films of layered crystals. Graphene, because of its extraordinary electronic properties, will be a major focus of this project. In view of application of graphene in electronics, we shall model electronic transport and dynamical properties of devices based upon epitaxial graphene (monolayer and bilayer), graphene deposited on atomically flat substrates, and chemically modified graphene. In the family of graphene, the bilayer allotrope is the less understood, though it has already been discovered to have quite unique electronic properties, and we shall develop theories of the electron-electron correlation effects, quantum transport and quantum Hall effect in bilayer graphene. But beyond graphene, we shall also investigate electronic properties of ultrathin films of hexagonal boron nitride on account of its insulating and optical properties, and on account of their use in hybrid devices such as graphene/h-BN based transistors. In parallel, we shall search for new opportunities in the world of two-dimensional materials beyond graphene. For this, we shall model theoretically electronic properties, correlations effects, optical properties, and electronic transport properties of single layers and bilayers of hexagonal transition-metal dichalcogenides with a broad range of composition and ultrathin films of bismuth-based trichalcogenides.