From N.S. Gill,
Your Guide to Ancient / Classical History.
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Definition: Admetus was a legendary king of Thessaly who lived during the time of Hercules. Admetus was doomed to die young, but Apollo, who had been made to serve Admetus for a year, during which time he grew quite fond of the king, arranged for Admetus to be saved from death, if someone would die in his place. When the parents of Admetus refused to give up their own lives for their son, Admetus criticized them for their selfishness, then turned to his own wife and the mother of his children. Alcestis nobly agreed to die for her husband.
Hercules came visiting Admetus while the house was in mourning for Alcestis, but Admetus claimed the dead was not a member of his family, and therefore no concern of Hercules'. When the servants revealed to Hercules that it wasn't a stranger, but the wife of Admetus who had died, Hercules went to Hades to rescue her.

The story of Alcestis and Admetus is told in Euripides' Alcestis.

Alternate Spellings: Admetos