Numerous members of the Adams administration, including the mayor himself, faced indictments or investigations. After Mr. Trump’s Justice Department abandoned the charges against Mr. Adams, apparently in exchange for his help with the president’s deportation agenda, the backlash quashed Mr. Adams’s diminishing hopes for re-election.

By some estimates, child care in New York City costs $15,000 to $20,000 per year. Many people are quite happy on Long Island.

Mr. Mamdani gives unacknowledged shout-outs here to former Gov. Mario Cuomo, Andrew Cuomo’s father, who spoke of poetry and prose, and to Ronald Reagan, who immortalized the image of a “shining city on a hill,” which he adapted from a 1630 sermon by John Winthrop, governor of the Massachusetts Bay Colony.

As of the 2020 Census, 40 percent of New Yorkers were foreign-born. The city has had at least two dozen immigrant mayors, most recently London-born Abraham Beame, who ran the city from 1974 to 1977 and oversaw the city’s fiscal collapse.

Many speculated that “turn the volume up” referred to a song by the rapper KRS-One. But Mr. Gerson, the speechwriter, said it did not.

Mr. Trump has incorrectly called Mr. Mamdani a communist and threatened to deport him or deny federal funds to New York City if he was elected. But after Election Day, the president said he might “help him a little bit maybe,” because he wanted New York City to succeed. Mr. Mamdani used Mr. Trump’s antagonism — and his support for Mr. Cuomo — as a talking point.

More than 20 billionaires contributed to super PACs opposing Mr. Mamdani, including Michael Bloomberg ($13.3 million), the Lauder family ($2.6 million), Joe Gebbia of Airbnb ($2 million), Bill Ackman ($1.75 million) and Barry Diller ($500,000). Mr. Mamdani has proposed a 2 percent tax increase on incomes of more than $1 million.

During the campaign and after, Mr. Mamdani has drawn criticism from some Jewish New Yorkers for his support for Palestinian rights and tepid condemnation of the slogan “globalize the intifada.” He has reached out to Jewish leaders to assuage their doubts.

Mr. Mamdani proposed this new city agency to help address crime through treatment for mental health and drug abuse, moving some responsibility away from police officers and to health care professionals.

The New York City Housing Authority, the city’s biggest landlord, manages over 177,000 apartments that are home to more than half a million legal tenants. The buildings need repairs and renovations totaling some $78 billion, according to the latest estimate by the authority.

La Guardia (1882-1947), a New Deal-supporting Republican who served three terms as mayor, sometimes referred to himself as a socialist.