As prospective jurors filed into the courtroom for jury selection, Donald Trump surveyed the group. One woman appeared to smile upon recognizing Trump. A man leaned forward and appeared to stare for several seconds.

"You've been summoned for possible service in a civil case," Judge Kaplan said before introducing the plaintiff and defendant. "This case is between a writer, advice columnist E. Jean Carroll, and former President Donald Trump," he said.

Jurors were told the case is expected to last three to five days and that they would sit through Thursday and, if necessary, return on Monday. They were also told they will be anonymous.

"That means neither your names nor the names of the jurors who are ultimately selected will be made public," Judge Kaplan said. He had earlier cited Trump's rhetoric as among the reasons for the anonymous jury.

Jurors will assemble daily at an off-site location and be driven to court under guard, the judge said.

"This is for your own protection. As you may understand, this case has attracted media attention and that's likely to continue," Kaplan said.

Unlike courtrooms where the counsel tables are arranged side by side, the counsel tables in the courtroom this morning are arranged behind one another, with Trump and his attorneys seated two tables behind Carroll and her counsel.

Trump appeared to take note of that arrangement when he entered the courtroom.

He appeared to point at Carroll, then he and his team asked a man seated at the table between them to slide over -- possibly to block Trump's view of Carroll, or to provide a better view of the proceedings.

On Friday, Judge Kaplan denied a request from Trump's attorneys to postpone the trial for a week so Trump could attend Thursday's funeral of Amalija Knavs, the mother of former first lady Melania Trump, who died last Tuesday after a long health battle.

In court this morning, Trump attorney Alina Habba repeated her request for an adjournment so Trump can attend Knavs' funeral.

"You asked me for a week's adjournment and I denied it," Judge Kaplan said. "The repetition is not accomplishing anything."

The judge said Friday that he would grant a continuance so the trial, which was initially scheduled to conclude this week, would be extended so Trump could testify on Monday, Jan. 22.

"The court has made a number of rulings precluding evidence and argument," said Judge Lewis Kaplan as court got underway, asking each side's lead attorney to affirm that the parties understood the rules.

The defense objected, arguing that the court lacked jurisdiction. Kaplan quickly dispensed with the objection, saying, "Overruled." Kaplan, who has a reputation as a no-nonsense judge, also overruled several other defense objections.

"I do think these are issues that will become an issue on appeal. We still don't know what witnesses are coming in and which aren't," Trump attorney Alina Habba said, before Kaplan interrupted, saying, "Ms. Habba you have had a witness list for months."

Habba pressed on, with Kaplan noting her objections.

"I have heard you, I have considered what you have to say and I have ruled," Judge Kaplan said.