Plasma spectroscopy had served as a fertile field for applications of the formalism of Dressed Atomic States in Plasmas (DASP). The theory named in the title of this paper is based primarily on a generalization of the formalism of DASP. In its contemporary composition, this theory brings together: A) non-impact description of the indirect coupling of the electron and ion microfields; B) non-binary description of the direct coupling of the electron and ion microfields; C) non-binary non-irnpact description of the ion-dynamical broadening. The latter produces, in particular, a new counter-intuitive result for the dependence of the Ion-Dynamical Stark Width (IDSW) on the temperature T: it predicts that in distinction to the high-T limit, for which it was known that IDSW similar to 1/T-1/2, in the low-T limit the temperature dependence changes to IDSW similar to T-1/4. In other words, as the temperature decreases from the high-T limit, the IDSW first increases similar to 1/T-1/2, then reaches a maximum, and then decreases similar to T-1/4 (this being a non-binary result). A non-binary result on the density dependence of the IDSW is also presented. The theory composed of the above items A), B), C), is used for creating extensive Tables of Stark widths of hydrogen lines in plasmas. By comparison with benchmark experiments, it is shown that these Tables are more accurate than the corresponding tables published previously by other authors.