Back in session: it's the first full year for the Supreme Court's new team, and there are some tough issues on the docket.

• Author: Greenhouse, Linda
• Position: John G. Roberts Jr. appointed

The Supreme Court is made up of just nine people with lifetime appointments, so changing even one can make a big difference, and for a long time. Last term, two new Justices joined the Court, including Chief Justice John G. Roberts Jr. The new term, which began last month, could give a clearer picture of the direction of the Roberts Court.

"I think this term is when the new Court is really going to define itself," says Jack Beermann, a law professor at Boston University.

Roberts assumed the leadership of the country's highest court in October 2005. Justice Samuel A. Alito Jr. took his seat four months later, replacing Justice Sandra Day O'Connor, the first woman on the Court.

Appointed by President Reagan in 1981, O'Connor was often the "swing vote" in cases decided by 5-to-4 votes. With O'Connor gone, Justice Anthony M. Kennedy appears to be emerging as the new swing vote.

There's also the possibility of further changes in the line-up: With four Justices over 70--including 86-year-old Justice John Paul Stevens, who has been on the Court for 31 years--President Bush may have the opportunity to make additional appointments in his last two years in the White House.

One of the most important decisions to come out of the last term was Hamdan v. Rumsfeld, which invalidated the system of military commissions Bush had set up for trying terrorism suspects held at the Guantanamo Bay naval base in Cuba. The Court said the commissions needed authorization from Congress, and that they violated the provision in the Geneva Conventions requiring humane treatment of prisoners, which the Court said does apply to terrorism suspects.

The decision was seen as a rejection of the Bush administration's broad interpretation of presidential powers. It prompted Congress to pass legislation in September spelling out procedures (which are also likely to be challenged in court) for how terrorism suspects will be tried.

Here are some important cases to watch this year:

* Racial Quotas in Schools. The Court will consider whether public-school systems can take race into account in assigning students to schools. It will hear challenges to policies in Louisville, Ky., and Seattle that use race as a factor in deciding which schools students attend as a way to maintain racial balance. The Bush administration is arguing that such race-based assignment plans are unconstitutional.

Three years ago, in a 5-to-4 decision in Grutter v. Bollinger, which involved admissions at the...