The Supreme Court begins its new term Monday. (Larry Downing/Reuters)

The Supreme Court begins its new term Monday under an ­election-year spotlight, with a chief justice who has become a campaign issue and a docket that seems designed to remind Americans about the importance of the high court in the presidential contest.

The nine justices enter the next decade of the Roberts court poised to confront issues that animate the political agenda: the legality of racial preferences to encourage diversity; how far government must go to accommodate religious liberty; how far government may go to restrict a woman’s right to abortion.

The last term ended on a high note for liberals, with a landmark decision finding a constitutional right for same-sex couples to marry. The term was the first since John G. Roberts Jr. debuted as chief justice 10 years ago that, in some of the court’s most closely contested and important decisions, the court’s liberal minority attracted one conservative or another to consistently prevail.

Few look for a repeat based on the issues the court will hear this term.

“I would expect a return to the norm, in which the right side of the court wins a majority, but by no means all, of the big cases,” said Irv Gornstein, head of the Supreme Court Institute at Georgetown Law Center.

“The big question for this term is, how big will the big wins be?”

The court already has a track record on the likely marquee cases of the term, and that record is giving the right a reason to be optimistic.

Back for further review are the affirmative-action remedies employed by the University of Texas to increase diversity at the flagship campus in Austin. The court has previously expressed its skepticism about these measures.

The contraceptives-coverage mandate of the Affordable Care Act is also making a return. The court already told the government last year, in Burwell v. Hobby Lobby, that the mandate impinged on the religious freedoms of some employers directed to carry it out.

And, because the court long ago decided that states may impose some restrictions on abortion, the question in a coming case will be, how far may they go before it becomes an “undue burden” on a woman’s right? The court has provided little guidance on what that term means.

The pivotal justice on each issue will probably be Justice Anthony M. Kennedy. The issues all appeal to Kennedy’s conservative side, but he does not always share the zeal for dramatic change that his colleagues on the right might pursue.

“I have the greatest respect for him, but I long ago gave up trying to predict him,” conservative U.S. Circuit Judge J. Harvie Wilkinson III said recently at a panel discussion at William and Mary Law School.

“The best thing you can do is issue one of those weather forecasts that says sunny with considerable clouds and a chance of rain.”

Conservatives long ago gave up on Kennedy as a reliable vote, but the surprise of the summer and fall is the suspicion with which many now view Roberts.

At the most recent debate of Republican presidential candidates, Sen. Ted Cruz (R-Tex.) bluntly called Roberts a ­“mistake.” Former Florida governor Jeb Bush said Roberts “did not have a proven, extensive record” when his brother, President George W. Bush, chose him, and he pledged that he would not make “politically expedient” choices for the court.

Dozens of conservative activists last weekend signed on to a letter from former attorney general Edwin Meese calling for the next president to appoint justices like Antonin Scalia, Clarence Thomas and Samuel A. Alito Jr. — no mention of Roberts.

The case against Roberts consists almost entirely of his votes upholding the Affordable Care Act. In 2012, he wrote the opinion turning down a constitutional challenge to President Obama’s signature domestic achievement. In June, Roberts and Kennedy were part of a 6-to-3 decision that rejected a reading of the law that would have drastically cut back the number of Americans it covered.

On the other side of the ideological ledger, Roberts has voted to restrict abortion rights, overturn campaign finance restrictions, recognize a Second Amendment right for individual gun ownership, and severely cut back the reach of the Voting Rights Act.

Studies have shown him to be one of the modern justices most protective of business interests. He is a consistent supporter of the death penalty, an issue that bitterly divides the court and which will be again be a common thread on the term’s docket.

Any change in even a single justice could tilt the balance of the court, and many predict that the next president may have the chance to nominate as many as three members of the court.

Liberal Justice Ruth Bader Ginsburg, Scalia and Kennedy will all be in their 80s on Inauguration Day 2017, and liberal Justice Stephen G. Breyer will be 78. The court currently has five Republican nominees and four chosen by Democratic presidents.

Ginsburg was the lone member of the court to find no fault with the University of Texas’s unique admissions policy when the court first considered it in 2013.

Most of the university’s freshmen are admitted under a plan in which the top students at every Texas high school are accepted. Because many of the schools are dominated by one ethnicity, this makes for a diverse population. To fill out the rest of the class, admissions officials say they use a holistic approach in which race is one of the factors considered.

An appeals court upheld the plan as being consistent with the Supreme Court’s previous rulings on when race could be considered. But the justices sent it back and told the lower court to demand more proof from University of Texas officials that they could not ensure diversity without resorting to racial classifications. The appellate judges again sided with the university, and challengers of the plan are returning to Supreme Court.

Kennedy has never ruled in favor of an affirmative-action plan, but he also has refused to join conservative colleagues in saying race can never be considered. Kennedy “really believes in the value of integration,” said Georgetown’s Gornstein, but at the same time “he desperately wants it to be achieved by race-neutral means.”

The court has yet to accept the abortion or contraception cases for this term, but they are considered highly probable.

The former case concerns new restrictions on abortion providers that have been enacted by states around the country, such as requiring doctors at abortion clinics to have admitting privileges at nearby hospitals and that clinics must meet surgical standards that abortion providers say are unnecessary and prohibitively expensive.

At issue is whether the standards put an undue burden on women seeking abortions, a standard the Supreme Court set in a 1992 case, Planned Parenthood of Southeast Pennsylvania v. Casey. Kennedy was one of the justices who set the standard.

The court is likely to look at Texas’s new law, and “I think it will be the most important case since Casey,” said Jennifer Dalven, director of the American Civil Liberties Union Reproductive Freedom Project.

“It will give us some guidance on the meaning of the undue burden standard and how courts should evaluate the multitude of abortion restrictions that are coming out of the states.”

The contraception case would be a sequel to the court’s decision last year that some private employers do not have to comply with the ACA mandate to provide employees with health plans that include contraceptives when this violates the owners’ religious beliefs.

This time, it is religious organizations such as hospitals, charities and universities that want to be freed from the requirement.

The Obama administration has provided an accommodation for objectors, which would allow them to object in writing and then have third-party insurers or the government step in to provide the cost-free care. But the organizations say any involvement violates their religious liberties.

Seven appeals courts have agreed with the government, but an eighth recently sided with challengers. That almost requires the court to settle the conflict, and the Obama administration recently also asked the court to step in.

Two other cases on the court docket also have partisan overtones.

One concerns whether public employee unions may collect a fee from nonmembers to cover the cost of collective bargaining. Challengers say that violates the First Amendment rights of those who don’t want to pay for union speech with which they disagree. The unions say the fees are warranted because unions are obligated to represent all public employees, whether or not they are union members.

The political context is that public employee unions, which overwhelmingly support Democratic candidates, are powerful players in elections. A loss would weaken them at the same time the court has made it easier for wealthy individuals and corporations to spend unlimited amounts on elections.

And a challenge to the way almost every state draws electoral districts presents a partisan dilemma. States use total population numbers from the census to meet a constitutional requirement that they are roughly balanced for “one person, one vote.”

But conservative groups are challenging that, saying the districts should be drawn based on the number of eligible voters in the districts. Most analysts say that would hurt urban areas with larger numbers of children and noncitizens — areas that are most likely to trend Democratic — and shift the power to more rural, less diverse areas that tend to vote Republican.

“Anytime the court is asked to engage in policing the electoral process, there is a risk of the results appearing to be partisan,” said David Cole, a law professor at Georgetown.