With her thesis advisor, historian Sean Wilentz, seated only a few feet away from her spot on the Richardson Auditorium stage, Elena Kagan was nervous — or so she joked. Since graduating in 1981 from Princeton University, where she was a history major not necessarily planning a career in law, Ms. Kagan has amassed a stellar legal resume culminating with her appointment four years ago to the United States Supreme Court.

Last Thursday, Ms. Kagan took part in a conversation at Richardson with University president Christopher Eisgruber. “I’m nervous he’ll take out his red pen,” she said, eyeing Mr. Wilentz in the audience. This was Ms. Kagan’s first visit to the University since her 25th reunion. “Don’t worry,” Ms. Eisgruber responded. “We’ve repealed the grading process.”

So began a congenial discussion about justice, equality, and human rights that ended with a question-and-answer session between Ms. Kagan and students in the audience. “I loved Princeton,” she said. “I think all of you who go to Princeton are incredibly lucky, at least if it’s anything like it was then, and I suspect it’s better. I had fantastic professors.”

After graduating from the University, the native New Yorker earned a master’s degree in philosophy from Oxford in 1983, and then graduated from Harvard Law School in 1986. She was Harvard Law School’s Dean from 2003 until 2009. Along the way, she served as Solicitor General of the United States, Associate White House Counsel to President Bill Clinton, Deputy Director of the Domestic Policy Council, and professor at the University of Chicago Law School.

Ms. Kagan said her colleagues received her warmly when she joined the court, where she had clerked as a young lawyer for Justice Thurgood Marshall. At 54, she is the youngest of the nine Supreme Court justices. Writing skills are important in the job, which she called “a good gig,” and she attributes her proficiency to her Princeton education. Not surprisingly given the average age of 68, the court isn’t the most technically savvy group, she said.

Asked to characterize her judicial philosophy, Ms. Kagan said, “I don’t think of myself as a philosopher. The way it works is that it’s a very back and forth kind of thing. I’m a big precedent person. I think really hard about how due process has changed over time.”

Ms. Kagan said that despite their different political leanings, the Supreme Court justices actually agree more than people might think. “Last year, 60 percent of our opinions were unanimous,” she said. But the 10 or so high-profile cases of the approximately 80 they take on are split “on pretty predictable lines.”

Ms. Kagan is often part of the liberal end of the court, with opinions sometimes splitting 5-4 along conservative to liberal lines. “Four of us think one thing and then four of us think the other thing. And then we wait and see what Justice (Anthony) Kennedy does,” she said, to laughter from the audience. Mr. Kennedy has often been the swing vote in decisions.

When Mr. Eisgruber asked Ms. Kagan if justices think about how their decisions can create political backlash, she responded, “It’s super rare that justices do or that they should. For the most part, you have a job to do, and your job is to apply the law as best you can.” She added that judges do have to think about how their decisions will be taken and avoid making them too hastily.

Asked whether there is corruption in the Supreme Court, Ms. Kagan said, “There is not a day in my job when I have ever thought anybody was not doing everything that they do in utter, complete good faith. You can disagree with people, and you will disagree with people, but everybody is trying to get it right.”