• President Trump’s inherited fortune.

“I built what I built myself,” Mr. Trump has often said.

But a special Times investigation, based on a vast trove of confidential tax returns and financial records, has found that his fortune is deeply connected to the riches of his father, the New York City builder Fred Trump. Above, father and son.

Mr. Trump was earning $200,000 a year from his father’s empire by age 3. He was a millionaire by age 8. He received at least $413 million in today’s dollars from his father in total.

Much of the money he received as an adult came from helping his parents dodge taxes — setting up sham corporations, filing improper deductions and even undervaluing real estate holdings by hundreds of millions of dollars, records and interviews show. Some schemes were outright fraud, the investigation found. Here are 11 takeaways.

A lawyer for Mr. Trump called the findings “100 percent false, and highly defamatory.” Read his full statement.