The first criminal trial of an American president will begin Monday as prosecutors and defense lawyers convene in a Manhattan courtroom to begin selecting the jury that will decide Donald J. Trump’s fate.

The Manhattan district attorney, Alvin L. Bragg, has charged Mr. Trump with 34 felonies, accusing him of falsifying documents to conceal a sex scandal involving a porn star.

The case, one of four indictments facing the former president and presumptive Republican nominee, could reshape the political landscape ahead of Election Day.

Jury selection could last two weeks or more and the trial may spill into June. Mr. Trump is expected to be in the courtroom for much of it, bringing campaign theatrics to the sober atmosphere of a criminal proceeding.

The spectacle will be remarkable: a former president face-to-face with a part of his past that he has tried to bury but that could instead make him a felon. In 2016, Mr. Trump’s former fixer, Michael D. Cohen, paid $130,000 to the porn star, Stormy Daniels, to buy her silence about a story of having had sex with Mr. Trump a decade earlier.

Mr. Trump, who might take the witness stand in his own defense, has denied the sexual encounter. But prosecutors say that he falsified a series of documents to hide reimbursements to Mr. Cohen.