The Supreme Court that Trump tilted to the right will review abortion, guns, and religion. Here are 5 important cases to watch as the new term begins.

• The new Supreme Court term begins Monday, loaded with explosive cases on the docket.
• Decisions on abortion and gun rights will show whether the court's expanded majority shifts the country to the right.
• The justices are also weighing in on legal battles involving religious liberty and the death penalty.
• See more stories on Insider's business page.

The Supreme Court returns to the bench on Monday with a number of explosive and high-profile cases on the docket.

From abortion to gun laws, the politically divisive cases will illuminate whether or not the court's expanded 6-3 conservative majority decides to dramatically shift the country to the right.

"They're the cases that will tell us the most of how quickly and how much the court moves in a more conservative direction," Lawrence Baum, a professor emeritus at Ohio State University whose expertise is the federal judiciary, told Insider.

The court will also take up cases involving religious liberty, the death penalty, state secrets, and more.

The session kicks off as the court faces all-time low public approval ratings, with a handful of the justices – Stephen Breyer, Amy Coney Barrett, Clarence Thomas and Samuel Alito – attempting to defend the court's legitimacy and independence.

The intense public scrutiny comes amid a contentious 5-4 ruling on September 2, in which the court's majority refused to block a strict Texas law that bans abortions after six weeks of pregnancy, prompting criticisms of partisanship.

Still looming over the new term is the coronavirus pandemic, with the court announcing on Friday that Justice Brett Kavanaugh has tested positive for COVID-19. The justices are expected to convene in person on Monday for the first time since the start of the outbreak last spring. Here are five big cases to watch for:

The court could throw out abortion rights

Nearly 50 years ago, the Supreme Court declared that women, protected by privacy rights under the 14th Amendment, have the right to an abortion. That 1973 landmark ruling, Roe v. Wade, legalized abortion until around 24 weeks of pregnancy, the point at which a fetus can survive outside of the womb, otherwise known as viability.

Yet that right could be threatened as the court evaluates a Mississippi law that prohibits nearly all abortions after 15 weeks of pregnancy.

Lower courts struck down the Mississippi statute, ruling that it violates Roe and Planned Parenthood v. Casey, the 1992 Supreme Court decision that declared states cannot impose an "undue burden" on abortion rights.

But Mississippi took its dispute to the highest court, which agreed to review the central question of whether state laws that prohibit pre-viability abortions are unconstitutional.

Arguments on the case, Dobbs v. Jackson Women's Health Organization, are set for December 1.

The court could expand gun rights and curtail regulations across the country

It's been over a decade since the court has considered a major gun-rights case. That will change on November 3, when the justices hear arguments on New York State Rifle & Pistol Association Inc. v. Bruen.

The case concerns a century-old New York law, upheld by the lower courts, that requires people who seek a license to carry a gun outside the home to demonstrate a "proper cause," or a special reason.

The National Rifle Association-backed challenge was brought by two New York men who applied for permits to carry a concealed gun in public for self-defense and were denied. They claim that the law is an infringement of the Second Amendment.

The Supreme Court will weigh in on "whether the state's denial of petitioners' applications for concealed-carry licenses for self-defense violated the Second Amendment."

Gun-control supporters worry that a Supreme Court ruling opposing the New York law may endanger firearm regulations amid a rise in gun violence across the country.

The court could narrow the separation of church and state

In Maine, some communities do not have public schools, so the state provides tuition assistance for students to attend private schools. In 2018, two families, the Carsons and the Nelsons, wanted to enroll their kids in private schools that offer religious teaching. They sought funding from the state but did not qualify, as the law requires the school to be "nonsectarian."

The families sued the state, arguing that the law violates their First Amendment right to exercise religion freely. A lower court ruled against their challenge.

The Supreme Court, which in recent years has protected religious liberties, took up their appeal. Justices will hear arguments on the case, Carson v. Makin, on December 8.

The ruling could have broad implications on the separation of church and state, as well as the hotly debated issue of "school choice." Proponents say school choice offers options beyond the traditional public school system, meanwhile critics say it erodes public schools, which most students in the country attend.

The court may reimpose a high-profile death penalty sentence

The Supreme Court is also slated to examine whether Dzhokhar Tsarnaev, the infamous Boston Marathon bomber who killed three people and injured hundreds in 2013, should be sentenced to death.

A federal appeals court dismissed Tsarnaev's death sentence last year, saying the judge who presided over the case in 2015 failed to ensure the jurors were not biased against him, calling into question the right to a fair trial under the Sixth Amendment.

Last October, President Donald Trump's Justice Department, which restarted federal executions after a 17-year pause, urged the Supreme Court to reinstate Tsarnaev's death penalty.

In June, the Biden administration asked the high court to do the same, despite President Joe Biden's campaign pledge to end capital punishment and pressure from some Democrats and civil rights organizations to abolish the practice.

The court will hear arguments on the case, United States v. Tsarnaev, on October 13.

The court will determine if the government can block information in a torture case

In United States v. Zubaydah, the court will review a request from a Guantanamo Bay prisoner seeking more information about his treatment by the CIA.

Abu Zubaydah, a terrorist suspect detained after the 9/11 attacks, was subjected in the early 2000s to what the CIA called "enhanced interrogation techniques." A Senate investigation later concluded the methods, which included waterboarding and confinement in a box, were torture.

Although Zubaydah's torture has been widely reported, he wants further disclosure from the CIA. But the government has blocked his efforts to subpoena CIA contractors, claiming "state-secrets privilege," a rule that allows the government to decline releasing information in a lawsuit that could risk national security. That standard was established in a 1953 landmark Supreme Court case, United States v. Reynolds.

A district court declined Zubaydah's case, upholding state-secrets privilege. A federal appeals court reversed the decision, arguing that some materials on his torture could be exposed. The Supreme Court will consider that court's ruling in arguments on October 6.