The following is a rundown of those parties expected to be the strongest contenders:
UNITED IRAQI ALLIANCE - List No. 555
The United Iraqi Alliance was formed with the blessing of Iraq's most influential Shia cleric, Grand Ayatollah Ali al- Sistani, to run in the first post-Saddam Hussein elections in January this year. It won overwhelmingly, securing almost half the vote, and remains Iraq's most powerful political group.
However, some parties have broken away since January and the Alliance goes into December's election slightly weaker than it was.
The list consists of 18 conservative Shia Islamist groups, although it is dominated by just three: current Prime Minister Ibrahim al-Jaafari's Dawa party, the pro-Iranian Supreme Council for the Islamic Revolution in Iraq, led by Abdul-Aziz al-Hakim, and the Iraqi nationalist Sadr movement, loyal to populist Shia cleric Moqtada al-Sadr.
Candidate posters for the many
parties contesting are going up
Al-Sistani has not explicitly backed the Alliance this time, but he has urged followers to vote for religious candidates and not to support weaker lists, an implicit endorsement of the Alliance.
Politically, the list stresses security, sovereignty and reconstruction, and has promised to crack down on the insurgency and corruption.
It was criticised for failing to tackle both issues during its past 10 months in office. The Alliance has also pledged to end government subsidies on basic goods and to provide families victimised by Saddam's rule with extra benefits.
KURDISTAN COALITION LIST - No. 730
The Kurdish coalition consists of eight groups but is dominated by the two main parties in the Kurdish north -the Patriotic Union of Kurdistan, headed by Iraq's current president, Jalal Talabani, and the Kurdish Democratic Party, headed by Masoud Barzani, the president of the semi-autonomous Kurdish zone.
The list won 75 seats in January's election, making it the second most powerful political bloc. It has been allied to the United Iraqi Alliance in government for the past 10 months, although the relationship is testy.
The Kurdish list's top priority is finding a solution for Kirkuk, a multi-ethnic city that sits atop vast oil reserves and which is claimed by Kurds, Turkish-speaking ethnic Turkmen and Arabs. They also vow to expand the Kurdish region's borders to include towns with historic Kurdish links.
IRAQI NATIONAL LIST - No. 731
The Iraqi National List pulls together 15 groups and is headed by Iraq's first post-war prime minister, Iyad Allawi, a secular Shia and former Baathist.
Former Iraqi PM Allawi is hoping
his secular party wins many seats
The list is secular in nature and pan-sectarian. It includes the Communist party, veteran Arab Sunni politician Adnan al-Pachachi, who was once foreign minister before Saddam came to power, major tribal figures and liberal Shia clerics.
The list won 40 seats in the 275-member parliament in January's vote and will look to increase its share as its secular message attracts more voters. The list vows to fight the insurgency and establish a strong central government.
They plan to revise the de-Baathification laws, brought in to rid all members of Saddam's Baath Party from office, and return more former officers in the Iraqi army, which was disbanded after the war, to the new security forces.
IRAQI ACCORDANCE FRONT - No. 618
The Iraqi Accordance Front is an alliance of three mainly Islamist Arab Sunni groups that boycotted elections in January.
The Front consists of Iraq's largest Sunni political movement, the Iraqi Islamic Party, which is running with a group called the Iraqi National Dialogue and an umbrella Sunni movement called the General Conference of the People of Iraq.
The Front pledges to push for the withdrawal of foreign forces, and promises security through dialogue and by bringing back former Iraqi army officers. Its leaders also want to change articles in the constitution especially wording on the devolution of power to Iraq's regions.
IRAQI NATIONAL CONGRESS LIST - No. 569
The Iraqi National Congress party is headed by deputy Prime Minister Ahmad Chalabi, the man who encouraged the United States to go to war in Iraq but has since fallen out with Washington.
Iraqi's will be choosing from some
231 parties in the vote
It groups 10 political parties and independents, including Sharif Ali, a relative of Iraq's last king. Chalabi split from the United Iraqi Alliance to form his group. The list stresses the need for Iraq to regain full sovereignty and to fight the insurgency by improving intelligence.
Chalabi has promised every Iraqi family a cash sum from Iraq's oil money and a piece of land for every family that does not own a home.
THE IRAQI FRONT FOR NATIONAL DIALOGUE - No. 667
List is headed by controversial Sunni politician Saleh al-Mutlak and includes Sunni Arab nationalists opposed to the government. Mutlak, a wealthy businessman, is a secular Sunni with links to Baathists close to the anti-US fighting. He promises to revise de-Baathification rules and return army officers to duty.