632: The Prophet Muhammad, founder of Islam, died. Abu Bakr, his father-in-law, became the first Caliph.
656-661: Ali, husband of Muhammad’s daughter Fatima, was the 4th Caliph.
661-680: Mu’awiya, who was not a member of the Prophet's family, was Caliph. He shifted the capital of the growing Muslim empire to Damascus.
680: Husayn, second son of Ali, was killed at Karbala.
The Sunni, the mainstream of Islam, derived from the people who accepted the legitimacy of Mu'awiya as caliph.
The Shi'i refused to accept Mu'awiya. They felt that a legitimate caliph could come only from the family of Ali and Husayn.
Important Sunni individuals and groups in Iraq today:
Arabs
Saddam Husain (secular)
Muslim Scholars Association
Al Qaeda in Iraq, led by Abu Mussab al-Zarqawi, a Jordanian (religious)
Kurds
Important Shi'a individuals and groups in Iraq today, all Arabs I think
The mainstream Shi'a leadership (religious)
Ayatollah Sistani
The Dawa Party, led by Prime Minister Jaafari
Supreme Council for Islamic Revolution in Iraq (SCIRI)
Moktada al-Sadr and the Mahdi (Mehdi) Army (religious)
Ahmad Chalabi (secular)
Former Prime Minister Allawi (secular)