Concepts and grounds One important area of research in modern material nanoscience concerns carbon-based materials, among which fullerenes take one of the œrst places. Nanochemistry of the twenty-œrst century, new light nanomagnets, new optical devices, new drugs-these and other excitedly sounded promises imply fullerene-based material can be heard throughout the world. What makes fullerene so exclusive for the properties of the materials to be outstanding? We shall try to answer this question from the viewpoint of computational nanoscience of fullerene. This consideration is based on the electronic properties of the molecule. Two cornerstones lay the foundation of the electronic fullerenics building. The œrst concerns the odd electron nature of the fullerene atomic system, which is intramolecular by nature. The second is the extremely high donor and acceptor characteristics of the molecules, and is intimately connected with intermolecular interaction that is smoothly transformed into the peculiar intramolecular property of fullerene derivatives and composites. It turns out that the two concepts make an allowance for interconnecting the fullerenics building constructions via tight interrelations between nanochemistry and nanomagnetism, nanomedicine and nanophotonics. In turn, the intrinsic concordance of the above building departments forms the ground for a uniœed theoretical approach. Before entering the building, let us look at the basic building blocks that form the construction fundamentals.