Among the key findings of The Times’s investigation:

Mr. Trump paid no federal income taxes in 11 of 18 years that The Times examined. In 2017, after he became president, his tax bill was only $750.

He has reduced his tax bill with questionable measures, including a $72.9 million tax refund that is the subject of an audit by the Internal Revenue Service.

Many of his signature businesses, including his golf courses, report losing large amounts of money — losses that have helped him to lower his taxes.

The financial pressure on him is increasing as hundreds of millions of dollars in loans he personally guaranteed are soon coming due.

Even while declaring losses, he has managed to enjoy a lavish lifestyle by taking tax deductions on what most people would consider personal expenses, including residences, aircraft and $70,000 in hairstyling for television.

Ivanka Trump, while working as an employee of the Trump Organization, appears to have received “consulting fees” that also helped reduce the family’s tax bill.

As president, he has received more money from foreign sources and U.S. interest groups than previously known. The records do not reveal any previously unreported connections to Russia.