Year after year, Mr. Trump appears to have lost more money than nearly any other individual American taxpayer, and the losses enabled him to avoid paying income taxes for eight of the 10 years. Here are five takeaways from our investigation.

How we know: The Times did not obtain Mr. Trump’s actual tax returns, which he has refused to release, but received the information from someone who had legal access to it. The information does not cover the tax years at the center of an escalating battle between the Trump administration and Congress.

Response: A lawyer for Mr. Trump, Charles Harder, said that The Times’s statements “about the president’s tax returns and business from 30 years ago are highly inaccurate.” He cited no specific errors but said that “I.R.S. transcripts, particularly before the days of electronic filing, are notoriously inaccurate.”

The Daily: In today’s episode, our reporters discuss the investigation.

Iran is to quit parts of nuclear deal

President Hassan Rouhani said today that his country would stop complying with two of its commitments under the 2015 agreement, which limited Iran’s capacity to produce nuclear fuel for 15 years.