With more than 11,000 tweets since taking office, Mr. Trump has used Twitter as a springboard to change policy, a cudgel against critics and an outlet for self affirmation. He has also elevated people whose words he finds pleasing and lent credibility to caustic views of conspiracy theorists, white nationalists and anti-Muslim bigots.

Quotable: “He needs to tweet like we need to eat,” Kellyanne Conway, the White House counselor, said of the president.

How we know: Times reporters analyzed Mr. Trump’s posts, studied the accounts he follows and interviewed administration officials, lawmakers, Twitter executives and ordinary Americans caught up in his tweets. Read nine takeaways from the investigation.