The new term’s biggest rulings will land in June, as the 2016 presidential campaign enters its final stretch, and they will help shape the political debate.

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WASHINGTON — The last Supreme Court term ended with liberal victories, conservative disarray and bruised relations among the justices. The new one, which opens Monday, marks the start of Chief Justice John Roberts’ second decade on the court and will reveal whether the last term’s leftward drift and acrimony were anomalies or something more lasting.

The court will decide major cases on politically charged issues, including the fate of public unions and affirmative action in higher education. It will most probably hear its first major abortion case since 2007 and revisit the clash between religious liberty and contraception coverage.

It will consider three cases that could make it harder for workers and consumers to band together in class actions.

And it will hear cases on the death penalty, a topic that twice led to unusually sharp and bitter exchanges on the bench last term, after Justice Samuel Alito accused opponents of capital punishment of pursuing a “guerrilla war” against executions. Justice Sonia Sotomayor responded that supporters of the death penalty would be content to allow condemned inmates to be burned alive.

Some of last term’s opinions were extra sharp even by the standards of Justice Antonin Scalia. Dissenting from the decision establishing a right to same-sex marriage, he called Justice Anthony Kennedy’s majority opinion pretentious, egotistic and incoherent.

Roberts, who has said he hopes to guide his court toward modest and unanimous rulings, cannot have enjoyed the rancor. Nor was his summer brightened by attacks on him from Republican presidential candidates unhappy with his sustaining of the Affordable Care Act for the second time.

The new term’s biggest rulings will land in June, as the 2016 presidential campaign enters its final stretch, and they will help shape the political debate.

“Constitutional law and politics are certainly not the same thing, but they are interrelated, never more so than in a presidential election year that will likely determine who gets to appoint the next justice or two or three,” said Vikram D. Amar, dean of the University of Illinois College of Law.

By the time the next president is inaugurated, Justice Stephen Breyer will be 78; Scalia and Kennedy will be 80, and Justice Ruth Bader Ginsburg will be 83.

“This coming term will again put into focus that the court is divided along partisan lines and that the 2016 presidential elections will be hugely consequential in shaping constitutional and other law for perhaps a generation or more,” said Neal E. Devins, a law professor at William & Mary.

The current court is the first in history split along partisan lines, where the party of the president who appointed each justice is a reliable predictor of judicial ideology. Put another way, all five Republican appointees are to the right of all four Democratic appointees.

It was not long ago that Republican appointees like justices John Paul Stevens and David Souter routinely voted with the liberal wing.

As a consequence of the current alignment, Devins said, “the Roberts court has generated more marquee decisions divided by party alignment than all other courts combined.”

The last term’s big cases did not for the most part follow that pattern because Kennedy, who was appointed by President Reagan and sits at the court’s ideological fulcrum, voted with the court’s liberal wing at an unusually high rate.

“The story of the last term is that the left side of the court did a lot of winning,” said Irving L. Gornstein, the executive director of Georgetown’s Supreme Court Institute.

“This term,” he added, “I would expect a return to the norm, with the right side of the court winning a majority, but by no means all of the big cases, with Justice Kennedy again the key vote.”

The cases on unions and affirmative action, for instance, were almost certainly added to the docket by the more conservative justices in the confidence that they would be able to move the law to the right.

The union case, Friedrichs v. California Teachers Association, No. 14-915, may deal a blow to organized labor. “It could set the stage for a Citizens United-style reconsideration in the area of union dues,” said John P. Elwood, a lawyer at Vinson & Elkins, referring to the 2010 decision that transformed campaign-finance law.

The new case takes aim at a compromise fashioned by the court in 1977 in Abood v. Detroit Board of Education.

In Abood, the court said public workers who decline to join a union can, nevertheless, be required to pay for the union’s collective-bargaining efforts to prevent freeloading and ensure “labor peace.” But nonmembers, it went on, cannot be forced to pay for the union’s purely political activities.

The California teachers who brought the new case say collective bargaining is itself political, as it concerns public policy on spending, seniority, class size and the like.

Unions respond that the case is a First Amendment Trojan horse designed to further weaken the power of organized labor.

The unions have reason to be nervous. The court has twice signaled that it may be ready to overrule Abood notwithstanding the doctrine of stare decisis, Latin for “to stand by things decided.” Alito, the court’s leading critic of Abood, offered a joking alternative definition in public remarks last month.

“It is a Latin phrase,” he said. “It means ‘to leave things decided when it suits our purposes.’ ”

The union case is not the only sequel on the docket.

In Fisher v. University of Texas at Austin, No. 14-981, the court will again take on whether the Constitution permits public colleges and universities to consider race in admissions decisions.

In 2013, the court refused to decide whether the school’s admissions plan — which combines race-neutral and race-conscious tools to achieve diversity — is constitutional. The court’s return to the subject after an appeals court sustained the hybrid plan has struck many supporters of affirmative action as an ominous sign.

The case was brought by the Project on Fair Representation, a small conservative advocacy group that successfully mounted a challenge to the Voting Rights Act in 2013. The group is also behind this term’s biggest case on voting, Evenwel v. Abbott, No. 14-940, which asks the court to address the meaning of “one person, one vote.”

The court has never resolved whether state voting districts should have the same number of people, including unauthorized immigrants, kids and others not eligible to vote, or the same number of voters. Letting states count only voters would in many parts of the country shift political power from cities to rural areas, benefiting Republicans.

On the last day of the term in June, Breyer and Ginsburg announced they had grave doubts about the constitutionality of the death penalty and seemed to invite a broad challenge. It has not yet arrived, and it is hardly clear that a majority would be receptive to such a challenge.

The new term does have an unusually high number of capital cases presenting more focused issues, including a challenge to Florida’s sentencing scheme, Hurst v. Florida, No. 14-7505, and a case on race discrimination in jury selection, Foster v. Chatman, No. 14-8349.

The court has not heard an abortion case since 2007, when it upheld the federal Partial Birth Abortion Ban Act. That seems about to change.

The most likely candidate is a challenge to a Texas law that threatens to reduce the number of abortion clinics in the state to about 10, down from more than 40.

Should the court agree to hear the case, Whole Woman’s Health Center v. Cole, No. 15-274, it is likely to produce the most important abortion ruling since 1992, when Planned Parenthood v. Casey reaffirmed the right to abortion identified in Roe v. Wade in 1973.

The question in the Texas case is whether two parts of a 2013 state law imposed an “undue burden” on the constitutional right to abortion. One part of the law requires all clinics in the state to meet the standards for “surgical centers.” The other requires doctors performing abortions to have admitting privileges at a nearby hospital.