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In a single finite electronic band the total optical spectral weight oroptical sum carries information on the interactions involved between the chargecarriers as well as on their band structure. It varies with temperature as wellas with impurity scattering. The single band optical sum also bears somerelationship to the charge carrier kinetic energy and, thus, can potentiallyprovide useful information, particularly on its change as the charge carriersgo from normal to superconducting state. Here we review the considerableadvances that have recently been made in the context of high $T_c$ oxides, boththeoretical and experimental.Comment: Review article accepted for publication in J. Low Temp. Phys. 29  pages, 33 figure

Optical Sum Rule in Finite Bands