Justice Sonia Sotomayor (top right) joins the Supreme Court for the new session
Cases involving US gun laws, videos depicting dog-fighting and the presence of a cross in the Mojave desert are among those expected to dominate a fresh session of the US Supreme Court which opens on Monday.
Justice Sonia Sotomayor is a new addition to the nine-member panel, replacing liberal Justice David Souter, who retired.
The court is expected to hand down rulings on the cases it considers in the spring.
Among the cases to watch out for are:
CHALLENGE TO GUN CONTROL LAWS
The Supreme Court justices have agreed to consider a challenge by gun rights activists to the city of Chicago's ban on handgun ownership.
The case is important because it will re-open the debate over the rights to bear arms under the Second Amendment of the US Constitution.
Last year, the court ruled by 5-4 that a ban on handguns in the capital, Washington DC, was unconstitutional - the first time it had considered the issue for almost 70 years - and that Americans have the right to own arms for personal use.
Since then, DC and other cities with strict gun control provisions, such as Chicago, have argued that it is not clear whether that ruling extends to state laws and city regulations too.
If the justices decide that Chicago's ban on handguns is also unconstitutional, the ruling could open the way for other challenges to state and local controls on who can own guns, whether they must be registered and how they are stored.
PRESENCE OF RELIGIOUS SYMBOL ON FEDERAL LAND
The Supreme Court will consider the case of an 8ft (2.5m) high Christian cross in the Mojave National Preserve, in California, which was put up as a monument to fallen World War I soldiers 70 years ago.
In 2003, a federal court ruled that because the cross stood on public ground, its presence violated a constitutional ban on the government endorsing one religion over another.
Congress tried to end the dispute by transferring the land to private ownership. But an appeals court ruled that the congressional action did not end the case.
The Supreme Court will look at whether the transfer of the land resolved the issue of the separation of church and state. It will also rule on whether the original plaintiff, a retired park service worker from Oregon, is entitled to bring the case.
The US Park Service has been forced to cover up the cross while the First Amendment legal arguments continue.
FREE SPEECH CHALLENGE OVER DOG-FIGHTING VIDEO
The court will consider whether the conviction of Robert Stevens for distributing videos depicting dog-fighting under a law aimed at curtailing animal cruelty violated his constitutional right to freedom of speech.
The 1999 law was intended to prevent depictions of animal cruelty, but a federal appeals court found that it restricted Stevens' right to free speech and threw out the conviction.
He argued that the videos were intended to educate people about the pit bull breed and that he was not trying to promote illegal dog-fighting.
The case has prompted debate over the restrictions that the government can place on free speech without falling foul of the First Amendment.
The nine-justice panel has already held a pre-term session to look at a case involving a 2008 documentary film, Hillary: the Movie, produced by the conservative group Citizens United.
The Federal Election Commission banned the film's release, saying it was an "electioneering communication" and that because it had been made with corporate funds, it was subject to restrictions under the 2002 McCain-Feingold campaign finance law.
The court may use the case to look at the wider issue of campaign finance and corporate spending.
Oral arguments in the case were first heard in March this year and the justices may seek an early decision so the rules are clear ahead of the 2010 mid-term elections.
CHALLENGE TO LIFE SENTENCES FOR JUVENILES
The justices will hear arguments as to whether it is legal to sentence a minor to life imprisonment without parole for crimes.
The challenge revolves around the Eighth Amendment's ban on cruel and unusual punishment.
It involves the separate cases of two minors in Florida, one aged 17 and one 13, who were each convicted of violent crimes and sentenced to life without the possibility of parole. The state of Florida rejected their appeals against the sentences.
The case follows a Supreme Court ruling in 2005 that defendants aged under 18 at the time they committed their crimes could not be sentenced to death.
CHALLENGE TO LAW MAKING IT A CRIME TO AID TERROR GROUPS
The court will examine whether a federal law that bans the provision of "material support to terrorism" is unconstitutional.
The law, which makes it a crime to give financial or other aid to any foreign group designated a terror organisation by the US, has been a central weapon in US anti-terror efforts.
The justice department has used it to prosecute more than 100 individuals, resulting in dozens of convictions, and it provides for sentences of up to life imprisonment.
First passed in 1996, the law was strengthened by the Patriot Act that was approved by Congress following the terror attacks of September 2001.
The groups and individuals who have challenged the law argue it that is unconstitutionally vague and bars support, including the provision of humanitarian aid, to legal, non-violent activities of designated organisations.
DISPUTE OVER HUMAN RIGHTS CASE AGAINST EX-SOMALIAN PM
The Supreme Court will consider whether a human rights case against former Somali Prime Minister Mohamed Ali Samantar should be allowed to proceed.
The lawsuit alleges that Mr Samantar, who now lives in the US state of Virginia, was responsible for killings, rape and torture while defence minister and prime minister under the authoritarian regime of Siad Barre in the 1980s and early 1990s.
A district court threw out the case in 2007, ruling that Mr Samantar was immune from prosecution under the Foreign Sovereign Immunities Act. But an appeals court disagreed, ruling that the law did not extend to individuals, only to countries and their agencies.
The justices will have to decide whether an individual acting in an official capacity for a foreign state is immune from prosecution.