It was 20 minutes into the first class of the semester when a professor of foreign policy at Columbia University halted the lecture. “I see the phones, and I see the cameras,” she said. “This is not a Taylor Swift concert.”

To avoid further disruption, the professor, Keren Yarhi-Milo, offered students a five-minute reprieve. They could raise their phones to photograph the celebrity co-teacher standing on stage, newly minted Professor Hillary Clinton.

“This,” Mrs. Clinton noted as hundred of cameras focused upon her, “is like the paparazzi,” a topic, like foreign policy, that she knows a great deal about.

Across New York City, students and teachers have returned from summer vacation this week. For Mrs. Clinton, 75, this marks her return to school after a much longer lapse. It has been nearly 50 years since her stint as a professor at the University of Arkansas Law School in Fayetteville, Ark.

On Tuesday, the day before her first lecture, Mrs. Clinton, a former secretary of state, U.S. senator and first lady, was setting up her office, which overlooks the campus from the 14th floor of Columbia’s International Affairs Building, and studying her binders of outlines and notes.

“I feel good,” she said in an interview in a conference room adjacent to her bright office, “but jittery.”

As is the case with most enterprises embarked upon by Mrs. Clinton — who has long been a sort of national Rorschach test, beloved by many and loathed by many others — her new gig carries greater meaning than simply a return to her academic roots.

The new job at Columbia may allow Mrs. Clinton to re-emerge publicly as a foreign policy expert, after years of being depicted in the press and the public’s imagination as the presidential candidate vanquished by Donald J. Trump.

For any liberal politician, but perhaps most of all for Mrs. Clinton — who years ago might have imagined herself in 2023 rounding out a historic presidency — there may be no softer landing ground than an Ivy League campus in New York City.

The class is offered through Columbia’s School of International and Public Affairs, a graduate school where tuition is more than $65,000 per year. “Inside the Situation Room,” as the class is called, is part of a broader partnership between Mrs. Clinton and Dr. Yarhi-Milo, the school’s dean and a professor of international relations who studies the psychology and mechanics of decision-making.

Together, the women are also establishing Columbia’s new Institute of Global Politics, where an inaugural group of fellows includes Marie Yovanovitch, the former U.S. ambassador to Ukraine; Stacey Abrams, the Georgia voting rights activist and former candidate for governor; and Eric Schmidt, the former CEO and chairman of Google. The fellows will work with students and scholars to mesh research and practical experience in the hopes of solving social and political problems on a global scale.

A spokeswoman for the public affairs school said that while other well-known figures, like Madeleine Albright, have been invited to teach on campus, few if any have been given the same mandate as Mrs. Clinton, who has been made a full professor in addition to her role with the institute. The spokeswoman declined to share details of Mrs. Clinton’s compensation or how it compared to that of other faculty members.

The class — named for the White House command center — is meant to deconstruct how choices with geopolitical consequences are made, through the lens of Dr. Yarhi-Milo’s data and Mrs. Clinton’s experiences. More than 800 students applied to take the class, submitting essays for consideration; about 370 graduate and undergraduate students were accepted. All were screened by the Secret Service.

Lectures will focus on topics like whether groups make better decisions than individuals and how public opinion influences foreign policy. Among the assigned readings: “How to Stand Up to a Dictator” by Maria Ressa, and sections from Mrs. Clinton’s 2014 memoir “Hard Choices,” in which she recounted her years as secretary of state during the Obama administration.

Students can expect Mr. Trump to come up only as he pertains to discussions of specific themes in diplomacy or historic instances of foreign policy, such as when he “pulled us out” of the Iran nuclear deal that was first negotiated by Mrs. Clinton.

“This class,” she said, “is not about him.”

Indeed, in the hourlong interview before her first class, as Mrs. Clinton discussed leaders from Vladimir Putin to Abraham Lincoln, it felt a million years away from today’s coarser public battles.

This year, she said, she is not following the Republican presidential primary closely. With polls pointing to Mr. Trump winning the nomination, she said, “I hope that people of good faith on all sides of the political divide understand what dire consequences there could be from him going back into the White House.” A spokesman for Mr. Trump, Steven Cheung, replied, “Hillary Clinton still can’t get over her devastating loss in 2016 and lives a miserable existence because she has to relive that glorious moment every single day.”

Mrs. Clinton said she did not bother watching the Republican primary debate on Fox News last month.

Why? “Summertime,” she said, and reflected on the season’s pursuits that brought her joy: Movies (“‘Oppenheimer,’” she said, “was extraordinary”); books (she stayed up until 3 a.m. reading Ann Patchett’s “Tom Lake”); and theater. Last Sunday, she took her three grandchildren to the “The Lion King” on Broadway. “There is nothing like seeing it with little kids,” she said.

Just four days later it would be Hillary Clinton on stage.

On Wednesday afternoon, students filtered into the Altschul Auditorium before the 2 p.m. class. It would be the first of Mrs. Clinton and Dr. Yarhi-Milo’s weekly lectures. Students are also expected to attend weekly discussion group meetings with teaching assistants, who will grade their assigned coursework.

Dr. Yarhi-Milo told the students that they would have no shortage of contemporary foreign policy crises to unwind: the war in Ukraine, the spy balloon that flew across the United States and tension in Taiwan, to name a few. To consider how leaders reacted, students would read and discuss game theory, behavioral psychology, time pressure and other elements that shape decisions. “That’s as much as I can tell you because I was not in the room,” she said.

Mrs. Clinton often was, and she shared several stories, including one that actually did take place in the Situation Room. In early 2009, after she had been nominated by then President-elect Barack Obama as secretary of state but not yet confirmed by the Senate, she received word from Condoleezza Rice, secretary of state under President George W. Bush, that she should report to the Situation Room.

Mrs. Clinton and other members of the incoming administration met with Bush officials, who briefed them on what they considered to be credible threats of attacks on the inauguration and Mr. Obama.

This was her first time in the Situation Room in an official capacity. “You’re pulled in; oftentimes you don’t know there is a crisis until you walk in the Situation Room,” she said. “It’s not yet in the headlines and sometimes it never is, which is not all bad.”

But being involved in high-level policymaking has its consequences, even years later. As Mrs. Clinton lectured students about how to make decisions, a small group protested outside the building, chanting, “Shame on you! Kick Hillary Clinton out!”

Dahoud Andre, an organizer with a group called Komokoda, said he hoped to pressure university officials to drop their relationship with Mrs. Clinton, who was secretary of state in 2010 when an earthquake ravaged Haiti. He believes the violence and political unrest that continues to plague the nation can be traced back to the response of the United States. A spokesman for Columbia declined to comment on the protest.

The President’s House

On Jan. 28, 2017, Mrs. Clinton found herself sitting down to dinner at a mansion built for presidents, more than 200 miles north of the White House where Mr. Trump had taken residence eight days before.

It was the President’s House at Columbia. She was there for a dinner in her honor hosted by Lee Bollinger, the longtime leader of the university, whom she has known for years.

After the 2016 election, he said, he wanted Columbia to be on her mind as she considered her future. Last year, as he was preparing to step down, everything fell into place. When Mrs. Clinton met with Dr. Yarhi-Milo, Mr. Bollinger said, “Everything lit up.”

At the end of class on Wednesday, students were invited to ask questions. One asked about gender disparities in foreign policy; another asked about the potential use of artificial intelligence in diplomacy.

Afterward, the students filed out of the auditorium and buzzed around a courtyard.

Akaysha Palmer, who is studying for a master’s degree in public administration, said she was glad that the discussion hadn’t included Mrs. Clinton’s loss to Mr. Trump. “I want to just focus on her role as secretary of state,” she said.

A fellow student, Bukuru Anastazie, concurred. “Her name is always attached to a man’s name,” she said. “It’s really refreshing just to have it be about her.”