Chemistry in the Final Stages of Stellar Evolution: Millimeter and Submillimeter Observations of Supergiants and Planetary Nebulae

High mass loss rates in evolved stars make them the major contributors to recycling processed material back into the interstellar medium. This mass loss creates large circumstellar shells, rich in molecular material. This dissertation presents millimeter and submillimeter studies of the end stages of low mass and high mass stars in order to probe their molecular content in more detail. In low mass stars, the molecular material is carried on into the planetary nebula (PN) stage. Observations of CS, HCO⁺, and CO in planetary nebulae (PNe) of various post-asymptotic giant branch ages have shown that molecular abundances in these objects do not significantly vary with age, as previously thought. More detailed observations of the slightly oxygen-rich PN NGC 6537 resulted in the detection of CN, HCN, HNC, CCH, CS, SO, H₂CO, HCO⁺ and N₂H⁺, as well as numerous ¹³C isotopologues. Observations of the middle-aged PN M2-48 showed the presence of CN, HCN, HNC, CS, SO, SO₂, SiO, HCO⁺, N₂H⁺, and several ¹³C isotopologues. These observations represent the first detections of CS, SO, SO₂, and SiO in any planetary nebula. The implications of these observations are discussed. A 1 mm spectral survey of the supergiant star NML Cygni has been carried out with the Arizona Radio Observatory Submillimeter Telescope resulting in the observation of 102 emission features arising from 17 different molecules and 4 unidentified features. The line profiles observed in this circumstellar shell are asymmetric and vary between different molecules, akin to what has been seen in another supergiant, VY Canis Majoris. The non-LTE radiative transfer code ESCAPADE has been used to model molecular abundances in the various asymmetric outflows of VY Canis Majoris, showing just how chemically and kinematically complex these supergiant circumstellar envelopes really are