The US Supreme Court has begun a new term, during which it will hear cases involving terror suspects' legal rights and the use of lethal injections.
The court will rule on the rights of inmates at Guantanamo Bay
The court will also review a state law requiring voters to show photo ID.
Observers are keen to see whether the highest US court continues the shift to the right it showed on divisive social issues in the term that ended in June.
The opening of the session coincided with the release of the memoirs of Supreme Court Justice Clarence Thomas.
In the autobiography, called My Grandfather's Son, Mr Thomas describes liberal interest groups who opposed his nomination to the court in 1991 as "left-wing zealots".
He also denounces a former aide who accused him of sexual harassment during his 1991 confirmation hearings.
In the new term, two cases involving the rights Guantanamo Bay detainees to challenge their indefinite detention in federal courts seem set to attract the greatest attention.
The cases, Boumediene v Bush and Al-Odah v US, are due to be heard in December.
The court rejected some 2,000 appeals filed over the summer
At issue is a 2006 law, passed by Congress and signed by President George W Bush, which stripped prisoners of the right to have their cases heard by federal judges.
Lawyers for the detainees say this violates their constitutional right to habeas corpus - a procedure under which someone who holds a prisoner is required to show reason why to a court. The administration disagrees.
The Supreme Court will also hear a challenge to the use of lethal injections as a method of execution brought by two death row inmates in Kentucky.
The men say the standard three-drug cocktail used violates the constitutional ban on cruel and unusual punishment.
The justices will also consider a case involving an Indiana state law requiring voters to show government-issued photo identification.
Another case concerns whether judges can use discretion in sentencing vendors of crack and powder cocaine. Guidelines call for significantly longer prison terms for sellers of crack cocaine, most of whom are black.
The Supreme Court also rejected some 2,000 appeals lodged over the summer.
One involved Guantanamo prisoner Salim Ahmed Hamdan, formerly Osama Bin Laden's driver in Afghanistan, who wanted his case to be heard with the others concerning Guantanamo Bay prisoners.
The court also declined to hear a dispute over whether some religious organisations can be forced to pay the costs of workers' contraception as part of their health insurance coverage.
The case was brought by Roman Catholic and Baptist groups, who argued that a law requiring them to offer contraceptives under their employee health insurance plans violated their constitutional right to free speech.
Another case rejected by the justices involved a request by US tobacco companies to consider making it harder for smokers to prove they were misled by the industry.
The appeal stemmed from a case in July 2006, when the Florida Supreme Court dismissed a $145 billion class action brought by 700,000 plaintiffs but upheld multimillion-dollar compensatory awards on behalf of two individual smokers.
The tobacco companies wanted to overturn the Florida Supreme Court's ruling that the findings against the companies could be used in individual suits by former members of the class action lawsuit.