Mr. Adams, the Democratic mayoral nominee, has stances on policing, transportation and education that suggest a shift from Mayor Bill de Blasio.In the afterglow of winning the Democratic nomination for mayor of New York City, Eric Adams began to set out his mission if elected in November.“Safety, safety, safety,” Mr. Adams said in one interview. “Making our city safe,” he said in another.On Thursday, as a torrential storm flooded the city’s subway stations, Mr. Adams offered another priority: Fast-track the city’s congestion pricing plan, which would charge fees to motorists entering Manhattan’s core, so that the money could be used to make critical improvements to the aging system.The two initiatives encapsulate Mr. Adams’s self-characterization as a blue-collar candidate: Make the streets and the subway safe and reliable for New York’s working-class residents.But they also hint at the challenges that await the city’s next mayor.To increase public safety, Mr. Adams has said he would bring back a contentious plainclothes anti-crime unit that focused on getting guns off the streets. The unit was effective, but it was disbanded last year amid criticism of its reputation for using excessive force, and for its negative impact on the relationship between police officers and the communities they serve.Congestion pricing was opposed by some state lawmakers, who wanted to protect the interests of constituents who needed to drive into Manhattan. But even though state officials approved the plan two years ago, it has yet to be introduced: A key review board that would guide the tolling structure has yet to be named; its six members are to be appointed by the Metropolitan Transportation Authority, which is controlled by Gov. Andrew M. Cuomo.Mr. Adams, who would be the city’s second Black mayor, would face other steep challenges: steering the city out of the pandemic; navigating the possibility of a new City Council trying to push him to the left; grappling with significant budget deficits once federal recovery aid is spent.How he intends to accomplish it all is still somewhat theoretical, but he has offered a few concrete proposals — some costly, and with no set ways to pay for them — mixed in with broader ideas.Some of New York City’s mayoral transitions have reflected wild swings from one ideology to another. The current mayor, Bill de Blasio, ran on a promise to end the city’s vast inequities, which he said had worsened under his billionaire predecessor, Michael R. Bloomberg. The gentle and consensus-building David N. Dinkins was succeeded by Rudolph W. Giuliani, a hard-charging former federal prosecutor.Privately, Mr. de Blasio supported Mr. Adams in the competitive primary, believing that he was the person best suited to carry on Mr. de Blasio’s progressive legacy, and if Mr. Adams defeats the Republican nominee, Curtis Sliwa, an abrupt change in the city’s direction is unlikely.But in some ways, Mr. Adams has staked out positions on issues like affordable housing, transportation and education that suggest a shift from Mr. de Blasio’s approach.On policing, Mr. Adams, who has pledged to name the city’s first female police commissioner, has already spoken to three potential candidates, and is believed to favor Juanita Holmes, a top official who was lured out of retirement by the current police commissioner, Dermot F. Shea. Mr. Adams has also vowed to work with federal officials to crack down on the flow of handguns into the city, and he has expressed concerns about how bail reform laws, approved by state lawmakers in 2019, may be contributing to a recent rise in violent crime.On education, Mr. Adams is viewed as friendly toward charter schools and he does not want to get rid of the specialized admissions test that has kept many Black and Latino students out of the city’s elite high schools, a departure from Mr. de Blasio’s stance. He has also proposed opening schools year-round and expanding the universal prekindergarten program by offering reduced-cost child care for children under 3.Transportation and safety advocates hope that Mr. Adams, an avid cyclist, will have a more intuitive understanding of their calls for better infrastructure. He has promised to build 150 new miles of bus lanes and busways in his first term, and 300 new miles of protected bike lanes, a significant expansion of Mr. de Blasio’s efforts.Increasing the supply of affordable housing was a central goal of Mr. de Blasio’s administration, and Mr. Adams supports the mayor’s highly debated plan to rezone Manhattan’s trendy SoHo neighborhood to allow for hundreds of affordable units.Mr. Adams has said he supports selling the air rights to New York City Housing Authority properties to help finance improvements to authority buildings. Hilary Swift for The New York TimesMr. Adams also supports a proposal to convert hotels and some of the city’s own office buildings to affordable housing units. The proposal originated with real estate industry leaders, who have watched their office buildings empty out during the pandemic.Mr. Adams favors selling the air rights above New York City Housing Authority properties to developers, an idea the de Blasio administration floated in 2018. Mr. Adams has said the sales might yield $8 billion, which the authority could use to pay for improvements at the more than 315 buildings it manages.Mr. Adams is viewed as pro-development — he supported a deal for an Amazon headquarters in Queens and a rezoning of Industry City in Brooklyn, both abandoned after criticism from progressive activists — and he was supported in the primary by real estate executives and wealthy donors.During his campaign, Mr. Adams met three times with the Partnership for New York City, a Wall Street-backed business nonprofit, according to Kathryn Wylde, the group’s president. Ms. Wylde expressed appreciation for Mr. Adams’s focus on public safety — a matter of great importance to her members — and confidence that he would be more of a check on the City Council, which she said was constantly interfering with business operations.“I think with Adams, we’ll have a shot that he will provide some discipline,” Ms. Wylde said. “Why? Because he’s not afraid of the political left.”Some of Mr. Adams’s stances have drawn criticism from progressive leaders like Representative Alexandria Ocasio-Cortez, who endorsed Maya Wiley in the Democratic primary.Alyssa Aguilera, an executive director of VOCAL-NY Action Fund, said that “having a former N.Y.P.D. captain in Gracie Mansion” only means “further protections and funding for failed law enforcement tactics.”“With that framework, it’s hard to believe he’s going to make any substantial changes to the size and scope of the N.Y.P.D. and that’s what many of us are hoping for,” Ms. Aguilera said.Mr. Adams, a former police officer, has expressed confidence that, under him, the Police Department could use stop-and-frisk tactics without violating people’s rights. Dakota Santiago for The New York TimesMr. Adams insists that even though he has been characterized as a centrist, he views himself as a true progressive who can meld left-leaning concepts with practical policies.To address poverty, for example, Mr. Adams has proposed $3,000 tax credits for poor families — an idea he said was superior to his primary rival Andrew Yang’s local version of universal basic income.“There’s a permanent group of people that are living in systemic poverty,” Mr. Adams said recently on “CBS This Morning.” “You and I, we go to the restaurant, we eat well, we take our Uber, but that’s not the reality for America and New York. And so when we turn this city around, we’re going to end those inequalities.”To deal with the homelessness crisis, Mr. Adams has proposed integrating housing assistance into hospital stays for indigent and homeless people, and increasing the number of facilities for mentally ill homeless people, especially those who are not sick enough to stay in a hospital but are too unwell for a shelter.Mr. Adams did not emphasize climate change or environmental issues on the campaign trail. But in his Twitter post about the subway flooding on Thursday, he called for using congestion pricing funds to “add green infrastructure to absorb flash storm runoff.”His campaign has pointed to initiatives from his tenure as borough president: helping to expand the Brooklyn Greenway, a coastal bike and walking corridor, not only for recreation but for flood mitigation; and improving accountability for the post-Hurricane Sandy reconstruction process. Those actions are dwarfed by the sweeping change he will be called on to oversee as mayor — particularly by a City Council with many new members who campaigned on a commitment to mitigate and prepare for the effects of rising seas and extreme weather on a port city with a 520-mile coastline.Mr. Adams expresses confidence that he can reinstate the plainclothes police squad and use stop-and-frisk tactics without violating people’s rights, contending that his administration can effectively monitor data related to police interactions in real time, and intervene if there are abuses.“We are not going back to the days where you are going to stop, frisk, search and abuse every person based on their ethnicity and based on the demographics or based on the communities they’re in,” Mr. Adams said on MSNBC last week. “You can have precision policing without heavy-handed abusive policing.”When some subway stations flooded on Thursday, Mr. Adams called for using money raised through a congestion pricing plan to make the system more resilient against bad storms. Fiona Dhrimaj, via ReutersMr. Adams seems most likely to differ from Mr. de Blasio on matters of tone and governing style.He is known for working round-the-clock, while Mr. de Blasio has been pilloried for arriving late to work and appearing apathetic about his job. Mr. de Blasio is a Red Sox fan who grew up in the Boston area and lives in brownstone Brooklyn; Mr. Adams, a lifelong New Yorker, was raised in Jamaica, Queens, by a single mother who cleaned homes. He roots for the Mets. Mr. Adams will come into office in a powerful position because of the diverse coalition he assembled of Black, Latino and white voters outside Manhattan.“De Blasio spoke about those communities; Eric speaks to the communities,” said Mitchell Moss, a professor of urban planning at New York University. “There’s a real difference. De Blasio was talented as a campaigner. Eric is going to be a doer.”Where Mr. de Blasio rode into City Hall as a critic of the police and a proponent of reform, he will end his term buried in criticism that he ultimately pandered to the department — a shift that many attribute to a moment, early in his tenure, when members of the Police Department turned their backs on him at an officer’s funeral.Officers were upset that Mr. de Blasio spoke about talking to his biracial son about how to safely interact with the police, a conversation that the parents of most Black children have. As mayor, Mr. Adams said he would gather with officers around the city for a different version of “the conversation.”“I’m your mayor,” Mr. Adams said he would tell officers. “What you feel in those cruisers, I felt. I’ve been there. But let me tell you something else. I also know how it feels to be arrested and lying on the floor of the precinct and have someone kick you in your groin over and over again and urinate blood for a week.”Mr. Adams will most likely be different from Mr. de Blasio in another way: He mischievously told reporters last week that he would be fun to cover. Indeed, he was photographed on Wednesday getting an ear pierced; the next day, he was seen dining at Rao’s, an exclusive Italian restaurant in Harlem, with the billionaire Republican John Catsimatidis.“He got his ear pierced and went to Rao’s,” Mr. Moss said. “He’s going to enjoy being a public personality.”Reporting was contributed by Anne Barnard, Matthew Haag, Winnie Hu, Andy Newman and Ali Watkins. More