Polybus (Ancient Greek: Πόλυβος) was king of Corinth and the adoptive father of Oedipus. Childless with his wife — named Periboea, Merope, or Medusa in different sources — he raised the exposed Theban infant as his own. Oedipus later fled Corinth to spare this kind father from the Delphic prophecy, not knowing Laius was his true sire. Distinct from Polybus of Ithaca and other mythic namesakes.
Adapted from Wikipedia, "Polybus of Corinth" · CC BY-SA 4.0
I.Adoption of Oedipus
When Laius and Jocasta exposed their infant on Cithaeron, versions disagree on the rescue: Periboea finds him while washing clothes; shepherds or Polybus' horse-keepers bring him to the queen; or Laius' servants give the child to the barren royal pair. With Polybus' consent they adopt him; after his swollen ankles are tended, he is named Oedipus. Some accounts add that Periboea later bore Polybus a daughter, Alcinoë.
II.The prophecy and death
Taunted that he is not Polybus' son, Oedipus consults Delphi and hears he will kill his father and marry his mother. Believing Polybus and Merope (or Periboea) to be his parents, he stays away from Corinth — and so meets Laius on the Phocian road. In Sophocles' Oedipus Rex a Corinthian messenger later reports Polybus' death by natural causes; Oedipus briefly thinks the prophecy void, until he learns Polybus was only his foster father.