Oedipus's fame comes from solving the riddle of the Sphinx.
Although Oedipus's name becomes a curse at the end of the tragedy, he is very confident and proud at the beginning due to the fact that he was the one that saved Thebas from the curse of the Sphinx. The Sphinx was a creature with the body of a lion and the head of a woman that posed a riddle to every traveller that tried to enter Thebas. Only when Oedipus arrived and solved the riddle did the Sphinx killed herself. In reward, he was crowned King of Thebas and he married the Queen without knowing she was actually his mother. Although at the end of the story he is famous for all the crimes he committed, at the beginning of the tragedy he is famous for his great achievement.
