The shell structure is a universal architectural principle that appears in many forms of matter, from planets to atoms. At the macroscopic level, the shells correspond to a set of concentric layers, forming a spherical structure. Such is the case for the earth itself, with a nucleus, a mantle and a crust. On the atomic scale the shell concept no longer refers to layers in space, but to layers in energy. Electrons are orbiting around nuclei, and while these orbitals may extend over the entire space, their energies are quantized and tend to cluster in shells. When the number of electrons is exactly right to fill a shell completely, a closed shell structure is obtained. These 'magic' electron counts are the hallmark of extra stability. They not only appear in atoms, but also in molecules. A well known class is the annulene family of molecular rings, with magic electron counts equal to 4n+2. The first and most studied member of this family, with n=1, is the benzene molecule, with special 'aromatic' properties. The underlying mathematical principles, which give rise to the shell concept, can also be applied in different dimensions and topologies and predict the existence of a wealth of other molecular families with their own magic counts. We refer to these as non-classical cases of aromaticity. In the project we investigate the electronic structures for some important non-classical families. One of the goals is the design and characterization of new types of aromatic molecules.