1. Introduction: attestations, p. 182 – 2. Previous scholarship, p. 183 – 3. Metrical analysis: ᵕ-ᵕᵕ is the original prosodic shape of ἀάατος, p. 194 – 4. Archaic oath formula in Ξ 271: the key passage for interpretation, p. 195 – 5. New solution: ἀᾱατος < *n̥ -seh₂u̯ n̥ to- ‘not lit by the sun’; ἀάατον Στυγὸς ὕδωρ is ‘sunless water of the Styx’, p. 197 – 6. Proto-Indo-European word for ‘sun’: *séh₂u̯ l̥, *s(h₂)u̯ éns and other forms, p. 198 – 7. Phonology: *ahāu̯ ato- > ἀάατο-: an Aeolic element in the Homeric diction, p. 202 – 8. Morphology: a bahuvrīhi with *séh₂u̯ n̥ to- ‘sunlight’ as a second member; *séh₂u̯ n̥ to- ← *suh₂ntó- ‘having sun’ (PGmc. *sunþa-, Toch. A swāñceṃ ‘ray of light’), p. 203 – 9. Semantics of ἀάατος and the gloomy Underworld of the Greeks, p. 209 – 10. Poetic status of *n̥ séh₂u̯ n̥ to- in Indo-European, p. 211: 10.1. Ved. asū́rta-; 10.2. YAv. axvarəta-; 10.3. YAv. x^vanuuant-, Gāth. x^və̄nuuant- – 11. Conclusion, p. 220 – Appendix: x^varənah-, the Avestan term for ‘glory’, p. 220.