The U.S. Supreme Court opened Monday for a new session that could tackle a number of major cases, including President Barack Obama's health care overhaul and a controversial immigration law in Arizona.

The nine justices will decide in the coming weeks and months whether to hear the constitutional challenges to President Obama's signature domestic policy. The new health care law, much of which has yet to come into effect, will be a prominent issue ahead of presidential and congressional elections in November next year, along with the issue of immigration.

The United States' highest court could also take up same-sex marriage, privacy rights and federal powers. It will also once again consider hearing oral arguments regarding affirmative action in college admissions and decide whether quotas can be used to determine college admissions.

The U.S. state of Arizona's controversial immigration laws will be considered for debate, as well as strict immigration laws in other states. Lower courts have limited or blocked some facets of the laws in some states. A Supreme Court decision would impact attempts by other states to reshape immigration policies.

Cases are presented for consideration by the justices during their nine-month session. Not all cases are guaranteed to be heard by the court. Once a case is presented before the Supreme Court, a decision is expected by June.