The accusations by the writer E. Jean Carroll that former President Donald J. Trump raped her and defamed her have been the subject of two separate trials in U.S. District Court in Lower Manhattan and have reverberated in Mr. Trump’s campaign for the Republican presidential nomination.

Last May, a jury found that Mr. Trump sexually abused Ms. Carroll, a former advice columnist for Elle magazine who said he assaulted her nearly three decades ago in a Bergdorf Goodman dressing room.

That same jury found he had also defamed her after he repeatedly denied the accusations and accused her of lying. Now, Mr. Trump, 77, is back in the same federal courthouse, defending himself again against accusations of defamation.

On Thursday, Ms. Carroll, the first witness in the case, ended her testimony in a trial that is expected to wrap up next week. It is still unknown whether Mr. Trump will take the stand.

Here’s a closer look at the two cases and what’s at stake.

Why were there two trials?

Ms. Carroll, 80, filed two lawsuits against Mr. Trump. The first, in 2019, accused the former president of making disparaging comments and branding her a liar in response to the publication of her book “Why Do We Need Men? A Modest Proposal.”

On June 21 of that year, Ms. Carroll published an excerpt from the book in New York magazine describing the assault.