We compare with theoretical models the properties of the brightest red stars in several aggregates in the Galaxy. Red giants and supergiants in the HR 1614 group (age approximately 3.5 x 10(9) yr) define in the H-R diagram a band whose slope in the M(bol) - log T(e) plane at low luminosities agrees with that of a theoretical curve defined by models consisting of an electron-degenerate helium core, a hydrogen-burning shell, and a hydrogen-rich envelope [first red branch (RGB) models]; at somewhat higher luminosities, the slope agrees with that of a theoretical curve defined by similar models (of constant mass) in which the electron-degenerate core is composed of carbon and oxygen [the quiescent hydrogen-burning phase of asymptotic giant branch (AGB) models]. In the models, the time-averaged luminosity increases monotonically with increasing core mass. The shallow slope of the AGB defined by the very brightest giants in each aggregate relative to the theoretical slope defined by constant-mass AGB models may be understood as a consequence of mass loss at a high rate from real AGB stars. The four brightest and reddest stars in the Hyades supercluster (which contains stars that were formed in bursts at different times in the past, the first burst occurring approximately 1.5 x 10(9) yr ago) exhibit characteristics which dovetail nicely with the characteristics of the four AGB stars in the HR 1614 group. The progenitors of the post-main-sequence stars in the supercluster are approximately 0.3-0.7 M. more massive than the most massive main-sequence stars in the HR 1614 group, and this accounts for the absence of an RGB in the supercluster; theoretical models more massive than some critical mass, which Hyades stars show to be approximately 1.6-2.1 M. Do not develop an electron-degenerate helium core and thus avoid the RGB phase. However, they do go through an extended phase of shell helium burning above an electron-degenerate core composed of carbon and oxygen and define an "early" AGB (EAGB) which is consistent with theoretical expectations. The fact that, in the supercluster, two AGB stars are carbon stars and one is an S star demonstrates that dredge up of freshly synthesized carbon following thermal pulses is occurring. This, coupled with the fact that none of the AGB stars in the HR 1614 group shows evidence for enhancement of surface carbon or of s-process isotopes, despite the similarity of initial composition, suggests that, at a given core mass, dredge up can occur only if the envelope mass above the carbon-oxygen core exceeds a critical value, in accord with theoretical expectations. Finally, the remarkable similarity in color, luminosity, and pulsation period of the Mira variables R Hya (a noncarbon star in the supercluster) and R Aqr (in the group) suggests that the masses of these two stars must be almost the same, giving additional evidence that there is not a single, unique age for supercluster stars, and demonstrating additionally that AGB stars lose mass at an evolutionary significant rate. Bright red stars in the old disk clusters NGC 2477 and NGC 2660 exhibit properties intermediate between those of similar stars in the HR 1614 group and the Hyades supercluster. In particular, the one AGB star in each cluster is a carbon star. Three of the four brightest and reddest stars in the very young disk clusters NGC 2516 and NGC 2287 (ages approximately 1 and 3 x 10(8) yr) are displaced substantially in the color-magnitude diagram from the bands defined by stars in the older aggregates; they are much bluer at a given luminosity. Member stars which are somewhat bluer still and dimmer are probably in the core helium-burning stage rather than in the EAGB stage, the brightest in NGC 2516 is probably a member of the younger component of this cluster (1 x 10(8) yr) and is in the EAGB stage, whereas the second brightest is probably a member of the older component and is in the TPAGB stage, having recently experienced a helium shell flash. Red giants in the globular cluster 47 Tuc (age approximately 10(10) yr, [Fe/H] = -0.6 dex) define two bands in the H-R diagram which are entirely analogous to those defined by HR 1614 group stars (age approximately 3.5 x 10(9), [Fe/H] = 0.1). The bands differ only in that the 47 Tuc bands are bluer, at a given brightness, than the HR 1614 bands, and the difference is quantitatively in accord with the theoretical expectations of band location with respect to metallicity. The "universal curve" defined by RGB and AGB stars in the HR 1614 group and in other old disk aggregates can be used to infer a distance to the Galactic center of 8.0 kpc, in reasonable agreement with other distance estimates. The Ba II stars in NGC 2420 and in the Wolf 630 group are bluer than stars of the same magnitude on the universal curve. This fact may be used in conjunction with an inferred true mass function for Ba II stars and in conjunction with theoretical properties of thermally pulsing AGB stars to infer that Ba II stars are red giants which have, as red giants, accreted of the order of 0.5 M. of s-process enhanced material from the AGB precursors of their companion white dwarfs.
