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Over the past several decades there have been major advances in our ability to evaluate computationally the electronic structure of inorganic molecules, particularly transition metal systems. This advancement is due to the Moores̕ Law increase in computing power as well as the impact of density functional theory (DFT) and its implementation in commercial and freeware programs for quantum chemical calculations. Improved pure and hybrid density functionals are allowing DFT calculations with accuracy comparable to high-level Hartree-Fock treatments, and the results of these calculations can now be evaluated based on experiment. When calculations are correlated to and supported by experimental data they can provide fundamental insight into electronic structure and its contributions to physical properties and chemical reactivity. This interplay continues to expand and contributes to both improved value of experimental results and improved accuracy of computational predictions. The purpose of this EIC Book is to provide state-of-the-art presentations of quantum mechanical and related methods and their applications by many of the leaders in the field. Part One of this volume focuses on methods, their background and implementation, and their use in describing bonding properties, energies, transition states and spectroscopic features. Part Two focuses on applications in bioinorganic chemistry and Part Three discusses inorganic chemistry, where electronic structure calculations have already had a major impact. This addition to the EIC Book series is of significant value to both experimentalists and theoreticians, and we anticipate that it will stimulate both further development of the methodology and its applications in the many interdisciplinary fields that comprise modern inorganic and bioinorganic chemistry