The son of Abdul Muttalib, grandfather of Muhammad. Thus Abbas is an uncle of Muhammad. He was a well-known Companion. Even more famous is his son Ibn Abbas who became an authority in relating hadiths and tafsir, the interpretation of the Qur'an. Abbas died A.H. 32.
The Abbasid dynasty, which held the Caliphate from 749/750 A.D. to 1258 A.D. was established by one of his descendants, and named after Abbas, since he was the family link to the Prophet from which they derived their legitimacy.