Adonis was the Greek god of beauty and desire. Nevertheless his origins are Semitic and is maybe based off the deity Tammuz.
His myth says that Aphrodite sheltered the baby Adonis and entrusted him to Persephone. Persephone fell in love with him and refused to give him back and the two goddesses started a dispute, only to be ceased by Zeus, who decided that the baby would be with each goddess one third of a year and the final third with the one he chose.
A boar would eventually kill him (believed to be sent by Ares) and Aphrodite would sprinkle his blood with nectar from which the anemone flower bloomed.
Adonis is a minor antagonist who's fought by Ayato at multiple points in the story.
He confronts Ayato for the first time in the Metropolitan Government Office. He sends out a Gamigin, Psyche, Dryad, Cupid, Melusine, and Hobgoblin before fighting Ayato and his party directly, but is ultimately defeated and forced to flee.
He's fought again in Harajuku Shelter, after Ayato, Sonoda, and Rui are forced to leave Pentagramma.
Afterwards, he challenges Ayato to a duel at Shinjuku Ground Zero Colosseum. Even though Ayato's allies are unable to help him, he's defeated again. Feeling humiliated after losing to Ayato a third time, he swears revenge and leaves.
He confronts Ayato for the final time in Bael's Castle, where he ultimately dies.