ASHINGTON, Oct. 5 — As the Supreme Court opens its new term on Monday, one obvious question is what the justices can possibly do for an encore.

In one amazing week in June, the court finished its last term with stunningly broad rulings upholding affirmative action and gay rights. Then last month, the justices assembled for a highly unusual special argument session on the constitutionality of the new campaign finance law, a case that counts as part of the past term. While it will be decided during the new term, no one outside the court knows whether a decision is days, weeks or months away.

Now it is back to business as usual — or almost usual. Because the first Monday in October coincides with Yom Kippur, the court will issue orders but will not begin hearing arguments until Tuesday. When all nine justices take the bench then, the public will be treated to the rare sight of a court entering its 10th term without turnover, the longest stretch of Supreme Court stability since the 12-year interval from 1811 to 1823.

The court has accepted 48 new cases for decision, filling its argument calendar through February and leaving room to hear and decide only about 30 more cases before the term ends in late June. The justices will meet weekly to continue the process of selecting cases from among many competing for their attention.

The court will soon decide, for example, whether to hear the Bush administration's appeal of a lower court decision barring the recitation of the Pledge of Allegiance in public school classrooms because of the phrase "under God." Another administration appeal seeks review of a ruling that doctors have a right to discuss with their patients the medical uses of marijuana.

In addition, cases challenging aspects of the detention policies the federal government adopted after the terrorist attacks of Sept. 11, 2001, have recently been filed or will shortly reach the court.

Of the cases already accepted for decision, three in addition to the campaign finance case stand out as raising questions of intensely practical as well as theoretical significance. They address issues of church and state, state versus federal power, and partisan politics.

The religion case, Locke v. Davey, No. 02-1315, raises the question of whether a state that offers taxpayer-financed scholarships for post-high school education can withhold the money from an otherwise eligible student who wants to use it to attend a religious college and major in theology. The case, to be argued on Dec. 2, is a natural, perhaps inevitable, successor to the Ohio school voucher case the court decided two terms ago. It held then that it is not an unconstitutional "establishment" of religion for the state to offer tuition subsidies that families, exercising their private choice, can apply toward parochial education.

While authorizing vouchers for religious education, that decision did not require them, and the pro-voucher movement has in fact encountered a major obstacle across the country. Most states, like the State of Washington in the new case, have provisions in their own constitutions that prohibit the use of public money for religious education. Overriding that provision, the federal appeals court ruled in this case that to withhold scholarship money on the basis of a student's religious choice places an unconstitutional burden on the free exercise of religion.

The two dozen briefs that have been filed in the case reflect a general awareness that the future of the school-choice movement could depend on the outcome. The Bush administration has entered the case to argue that Washington's refusal to subsidize religious training while paying for other higher education options is unconstitutional.

The new term's major federalism case challenges the enforceability of a central provision of the Americans With Disabilities Act, the requirement in the statute's Title II that public "services, programs or activities" be accessible to people with disabilities. In Tennessee v. Lane, No. 02-1667, Tennessee is claiming constitutional immunity from lawsuits challenging the state's failure to make its courthouses available to people using wheelchairs. One plaintiff, George Lane, had to crawl up two flights of stairs to make a required court appearance, and the other, Beverly Jones, is a court reporter who could not gain access to four courthouses where lawyers had hired her to record the proceedings.

Two years ago, the justices ruled that states could not be sued by their employees under the section of the disability law that bars employment discrimination. While Tennessee invoked that precedent in the new case, a federal appeals court ruled that access to court is itself a fundamental right that put this case on a different plane and trumped the state's immunity claim.

Last term, retreating from its recent insistence on state immunity, the court permitted suits against states under the Family and Medical Leave Act. So the Tennessee case, to be argued in January, is being closely watched for evidence of broader trends in the court's approach to federalism issues.

The political case on the court's docket is both highly political and, given the new Republican strategy of accelerating redistricting battles in order to maximize partisan advantage, highly relevant. The question is what standard courts should use in deciding whether a partisan gerrymander goes so far as to be unconstitutional.

The case, Vieth v. Jubelirer, No. 02-1580, is an appeal by Pennsylvania Democrats, who account for about half the state's voters but who hold only 7 of the state's 19 Congressional districts after redistricting in 2002. The Democrats are invoking a 1986 Supreme Court decision that held that a partisan gerrymander so severe as to thwart majority will violates the Constitution's guarantee of equal protection.

While that precedent is indisputably on the books, there is great dispute over how it should be applied in practice and how actively the federal courts should intervene in partisan politics. The federal court in this case said the precedent should be applied only when one party was "completely shut out of the political process." The Democrats argue that this hands-off stance invites "severe distortions of the democratic process." The case will be argued on Dec. 10.

Even in the absence of any post-Sept. 11 cases, the new term already appears likely to include important developments in criminal law. Several cases offer new twists on a staple of search-and-seizure law, encounters between the police and people in cars.

In addition, two cases to be argued on Dec. 9 involve failure by the police to give suspects the warnings required by the court's Miranda rule. Both raise questions about common police interrogation tactics and about the scope of the court's decision three years ago, in Dickerson v. United States, that reaffirmed and strengthened the Miranda precedent.

One new Miranda case, Missouri v. Seibert, No. 02-371, examines an increasingly popular tactic by which the police first get a statement without Miranda warnings and then administer the warnings and obtain a confession. The issue is whether such a confession, even if preceded by a "voluntary" waiver of a suspect's Miranda rights, can be used as evidence when the original failure to give the warnings was deliberate.

The question in the second Miranda case, United States v. Patane, No. 02-1183, is whether physical evidence discovered as a "fruit" of a Miranda violation, a gun in this case, can be introduced at trial. Earlier Supreme Court decisions had permitted this type of evidence to be used under some circumstances, but lower courts are finding those decisions questionable in light of the justices' subsequent clarification in the Dickerson case that the Miranda warnings are constitutionally required rather than just a "prophylactic" device to safeguard the Fifth Amendment right against compelled self-incrimination.

By coincidence, three cases on the court's criminal docket involve defendants named Banks. In Banks v. Dretke, No. 02-8286, to be argued on Dec. 8, a Texas death row inmate, Delma Banks Jr., who came within 10 minutes of execution before the court granted a stay last March, is raising issues of prosecutorial misconduct and defense inadequacy.

The question in United States v. Banks, No. 02-473, to be argued on Oct. 15, is whether federal agents violated Lashawn L. Banks's rights by breaking into his apartment to look for drugs only 20 seconds after knocking on the door. And Beard v. Banks, No. 02-1603, is an effort by Pennsylvania to reinstate a death sentence for George E. Banks, convicted of multiple murders 20 years ago. No argument date has been set.