The US Supreme Court is back in session Monday to tackle major social issues such as same-sex marriage and affirmative action, as well as a high-profile international human rights case.

On its first day back in session, the highest US court will start off by reexamining a suit, alleging complicity in acts of torture, against Dutch oil giant Shell in Nigeria.

Twelve Nigerians accuse Shell of becoming an accomplice to torture, extrajudicial executions and crimes against humanity in the Niger Delta region.

The nine justices will decide whether to hold major companies liable for crimes committed outside US borders by virtue of the Alien Tort Statute, a law passed two centuries ago.

"ATS clearly covers those violations," said Carey D'Avino, one of the plaintiffs' attorneys. "There's nothing in the ATS that violates domestic and international laws."

Not everyone is so sure.

The Supreme Court could be "afraid of some kind of backlash, what other nations will think of us," said constitutional lawyer Lisa Blatt.

In what could be the term's most prominent case, the justices will take up affirmative action at the University of Texas.

The policy, aimed at correcting historic imbalances in education by favoring US minorities in public university admissions and other circumstances, has come under increasing scrutiny in the wake of a growing minority population.

A white student is accusing the university of using quotas for racial and ethnic minority groups in university admissions in a way she claims violates her US constitutional rights.

It will be the first time the court takes up the controversial issue since its 2003 ruling saying racial or ethnic quotas did not violate the US Constitution.

But since then, the makeup of the court has changed to make it "the most conservative in a lifetime," giving greater likely voice to affirmative action opponents, said Georgetown Law professor Louis Seidman.

Alan Morrison of The George Washington University Law School stressed that "there's a lot at stake and plenty of reasons to be concerned." He called the affirmative action decision "crucial," saying it would be felt at all US universities, both public and private.

Among the fairly rare national security issues to come before the court will be a case on wiretapping and human rights due to be examined on October 29. And on October 31, the justices are set to address whether the use of drug-sniffing dogs violates constitutional rights.

Still, in terms of social reach, it is the court's looming moves on same-sex marriage that have both captured a lot of Americans' attention and fueled strong reactions.

All eyes will be riveted on the court when it takes up any of at least eight appeals in line for consideration.

Justice Ruth Bader Ginsburg herself has said that "it's most likely that we will have that issue before the court toward the end of the current term."

James Esseks of the American Civil Liberties Union rights group suggested the court will agree in November to take up some months later the Defense of Marriage Act (DOMA), a law that defines marriage as a legal union of a man and woman.

The case addresses federal rights granted to heterosexual spouses -- such as inheritance rights, tax benefits and immigration rights -- but denied to same-sex couples, even though they are legally wed in several US states.

Attorney Paul Smith said the court would act now on gay marriage. "It is very, very likely they will take one (case). It would create an enormous chaos not to take one."

Neal Katyal, a former top US government attorney under President Barack Obama, said "the court has to take DOMA but they don't have to take Prop 8," referring to California's same-sex marriage law.

Republicans reject charges that DOMA violates the due process clause of the Fifth Amendment of the US Constitution.

After long side-stepping the issue, Obama put his reelection bid on the line by publicly endorsing gay marriage in May in a surprise move designed to draw a sharp contrast with Romney, his Republican rival who opposes same-sex unions.

Legal marriage between two men or two women is not recognized by the US federal government but is now allowed in six of the 50 US states and in the capital, Washington.