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Nuclear many-body theory provides the foundation for understanding and exploiting the new generation of experimental probes of nuclear structure that are now becoming available. The twentieth volume of Advances in Nuclear Physics is thus devoted to two major theoretical chapters addressing two fundamental issues: understanding single-particle properties in nuclei and the consistent formulation of a relativistic theory appropriate for hadronic physics. The long-standing problem of understanding single-particle behavior in a strongly interacting nuclear system takes on new urgency and sig- nificance in the face of detailed measurements of the nuclear spectral function in (e, e'p) experiments. In the first chapter, Mahaux and Sartor confront head-on the ambiguities in defining single-particle properties and the limitations in calculating them microscopically. This thoughtful chapter provides a thorough, pedagogical review of the relevant aspects of many- body theory and of previous treatments in the nuclear physics literature. It also presents the author's own vision of how to properly formulate and understand single-particle behavior based on the self-energy, or mass operator. Their approach provides a powerful, unified description of the nuclear mean field that covers negative as well as positive energies and consistently fills in that information that cannot yet be calculated reliably microscopically by a theoretically motivated phenomenology. Particular emphasis is placed upon experiment, both in the exhaustive comparisons with experimental data and in the detailed discussion of the relations of each of the theoretical quantities defined in the chapter to physical observables.