We present high-resolution (FWHM D0.4È1.8 km s~1) spectra, obtained with the AAT UHRF, the McDonald Observatory 2.7 m spectrograph, and/or the KPNO feed, of interstellar K I coude coude absorption toward 54 Galactic stars. These new K I spectra reveal complex structure and narrow, closely blended components in many lines of sight. Multicomponent Ðts to the line proÐles yield estimates for the column densities, line widths, and velocities for 319 individual interstellar cloud components. The median component width (FWHM) and the true median separation between adjacent components are both km s~1. The median and maximum individual component K I column densities, about [1.2 4 ] 1010 and 1012 cm~2, correspond to individual component hydrogen column densities of about 2 ] 1020 and 1021 cm~2 and E(B[V ) D 0.03 and 0.17, respectively. If T is typically D100 K, then at least half the individual components have subsonic internal turbulent velocities. We also reexamine the relationships between the column densities of K I, Na I, C I, Li I, and CH. The four trace H tot , H 2 , neutral species exhibit essentially linear relationships with each other over wide ranges in overall column density. If C is uniformly depleted by 0.4 dex, then Li, Na, and K are each typically depleted by 0.6È0.7 dex. The total line of sight values for N(K I) and N(Na I) show roughly quadratic dependences on but the relationships for the ensemble of individual clouds could be signiÐcantly steeper. These N(H tot ), quadratic (or steeper) dependences appear to rule out signiÐcant contributions to the ionization from cosmic rays, X-rays, and/or charge exchange with C II in most cases. Charge exchange with negatively charged large molecules may often be more important than radiative recombination in neutralizing most singly ionized atomic species in cool H I clouds, howeverÈsuggesting that the true and thermal n e , n H , pressures may be signiÐcantly smaller than the values estimated by considering only radiative recombination. Both N(CH) and are nearly linearly proportional to N(K I) and N(Na I) [except for 1015 N(H 2 ) cm~2, over which makes the transition to the self-shielded regime]. Those cm~2 [ N(H 2 ) [ 1019 H 2 relationships appear also to hold for many individual components and component groups, suggesting that high-resolution spectra of K I and Na I can be very useful for interpreting lower resolution molecular data. The scatter about all these mean relationships is generally small dex), if certain con-([0.1È0.2 sistently "" discrepant ÏÏ sight lines are excludedÈsuggesting that both the relative depletions and the relative ionization of Li, C, Na, and K are generally within factors of 2 of their mean values. Di †erences noted for sight lines in Sco-Oph, in the Pleiades, near the Orion Trapezium, and in the LMC and SMC may be due to di †erences in the strength and/or shape of the ambient radiation Ðelds, perhaps ampliÐed by the e †ects of charge transfer with large molecules.