This graduate level text presents the first comprehensive overview of modern chemical valency and bonding theory, written by internationally recognised experts in the field. The authors build on the foundation of Lewis- and Pauling-like localized structural and hybridization concepts to present a book that is directly based on current ab-initio computational technology. The presentation is highly visual and intuitive throughout, based on the recognizable and transferable graphical forms of natural bond orbitals (NBOs) and their spatial overlaps in the molecular environment. The book shows applications to a broad range of molecular and supramolecular species of organic, inorganic and bioorganic interest. Hundreds of orbital illustrations help to convey the essence of modern NBO concepts for those with no extensive background in the mathematical machinery of the Schroedinger equation. This book will appeal to those studying chemical bonding in relation to chemistry, chemical engineering, biochemistry and physics.