This handbook is intended to be a guide (a guide for the perplexed) for all scientists active in fields related to the above topic. The range of applications of electric polarizabilities and hyperpolarizabilities has dramatically expanded in recent years. Very active fields where the theory of electric polarizability is of primary importance are as mentioned below. Nonlinear Optics and the search for new materials with potential applications in Molecular Electronics and Optoelectronics - the design of molecules with specific characteristics relies strongly on reliable determinations of the molecular hyperpolarizability. Simulation Studies - in this rapidly expanding field the use of very accurate polarizability and hyperpolarizability values is a key factor to the success of the simulation. Scientists are always seeking reliable data for their studies. The absence of any systematic presentation of such data constitutes a major problem, as readily evidenced in all related publications that have appeared recently in major journals. The handbook will provide recommended values for a very large number of systems of interest. A Database of such values will be an essential part of this endeavour. Spectroscopy - this represents a very wide spectrum of activities relevant to fields that rangefrom Atmospheric Chemistry to Surface Science. The main reason lies in the central importance of the theory of electric polarizability to major tools as Raman spectroscopy. Scientists active in Collision - and Interaction induced Spectroscopy lean heavily on the available polarizability mid hyperpolarizability values for the systems involved in such studies. It should be emphasised that the handbook will not include extensive presentations of theoretical or experimental methods. Such treatments are easily found in specialised textbooks. Emphasis will be given to the presentation of fields of application and the emerging new ideas. The most important part of the handbook will be the critical evaluation of the available data and the systematic presentation of the reliable data for large classes of systems, including atoms and almost all currently of interest molecules, in such a way that they will be readily accessible for potential applications. Primary audience for the work: Scientist at all levels - Researchers, Graduate Students, Undergraduate Students active in a wide spectrum of fields. These fields include Computational Quantum Chemistry, Spectroscopy, Simulation Studies, Molecular Physics. Nonlinear Optics and Materials Science: Secondary Market - the book will contain material relevant to various other fields as Medicinal Chemistry, Environmental Physics and Chemistry, Inorganic Chemistry. Scientists active in these fields are always interested in obtaining accurate polarizability values for use in various applications.