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When initially introduced, the reduced density matrices (RDMs) held the promise of greatly simplifying electronic structure calculations. Although these expectations were not met immediately, recent work has placed RDMs at the center of new approaches to the electron correlation problem. Many-Electron Densities and Reduced Density Matrices presents these exciting new developments that underscore both the relevance and practical applications of RDMs. This volume, put together by leading experts in the field, covers topics ranging from fundamental theorems describing mathematical structures of many-electron densities and reduced density matrices to new electronic structure methods that open an avenue to highly accurate atomic and molecular simulations. Many-Electron Densities and Reduced Density Matrices will be useful primarily to quantum and theoretical chemists, and solid state theorists, but also to physical, mathematical, and computational chemists. In addition to being a valuable resource for researchers, Many-Electron Densities and Reduced Density Matrices will find a place as a textbook in special topic courses at the advanced graduate level.