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Inductance is one of the fundamental defined parameters in electromagnetics and it takes on a variety of formulations and definitions in the electromagnetic compatibility (EMC) community. The concept of inductance in its many definitions, uses, and caveats was central among Dr. Clayton R. Paul's contributions to the EMC community. In this paper, we discuss the various aspects of inductance which Dr. Paul helped to pioneer. In particular, the concepts of partial inductance and internal inductance (including skin effect) were two of his passions. This paper will both serve as a summary of Dr. Paul's work on inductance as well as show how his work helped pioneer new research in this area.