This volume gives larger and deeper coverage of the electronic matters through the physical, chemical and biological ordered systems. With their increasing complexity, the matter structure from the physical to chemical to biological manifestations in an inter-disciplinary cross-fertilisation manner is gradually introduced. The book presents and reviews the avant-garde contributions for the XXI century with equilibrated contents provided by important scientists world-wide demonstrating a valuable impact on quantum fundamentals and applications. In fact, the present volume attempts to serve the unification of the physical-chemical-biological manifestation of atoms in molecules and in nanostructures by means of expanding the quantum frontiers by conjunction, either with relativity, topological information or graph theories as well.