MEXICO CITY — Claudia Sheinbaum was sworn in Tuesday as Mexico’s first female president, riding the enthusiasm over her popular predecessor’s social programs but also facing challenges that include stubbornly high levels of violence.

After a smiling Ms. Sheinbaum took the oath of office on the floor of Congress, legislators shouted the feminine form of the word president in Spanish — “Presidenta! Presidenta!” — for the first time in over 200 years of Mexico’s history as an independent country.

The 62-year-old scientist-turned-politician takes the reins in a country with a number of immediate problems, also including a sluggish economy, unfinished building programs, rising debt and the hurricane-battered resort city of Acapulco.

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“Now is the time of transformation, now is the time of women,” she said.

Ms. Sheinbaum romped to victory in June with nearly 60% of the vote, propelled largely by the sustained popularity of her populist political mentor, former President Andres Manuel Lopez Obrador. She has pledged to continue all his policies, even those that critics say strengthened the power of the military and weakened the country’s institutional checks and balances.

Mr. Lopez Obrador took office six years ago and promising historical change from the neoliberal economic policies of his predecessors. Mr. Sheinbaum promised continuity from his popular social policies to controversial constitutional reforms to the judiciary and National Guard pushed through during the ruling Moreno party in his final days in office.

Despite her pledge of continuity, Ms. Sheinbaum is a very different personality: a cautious scientist and ideological university leftist, as opposed to the outgoing president’s chummy, everyman appeal.

“Lopez Obrador was a tremendously charismatic president, and many times that charisma allowed him to cover up some political errors that Claudia Sheinbaum will not have that possibility of doing,” said Carlos Perez Ricart, a political analyst at Mexico’s Center for Economic Research and Teaching. “So, where Lopez Obrador was charismatic, Claudia Sheinbaum will have to be effective.”

She will, however, wield formidable power because Morena controls both houses of Congress. And with that come warning signs, because the country remains deeply polarized between the outgoing president’s fanatic fans and almost one-third of the population who deeply resent him.

“If we want a strong government, the checks and balances also have to be strong,” said opposition Sen. Maria Guadalupe Murguia, suggesting that an all-powerful army and unchecked ruling party could come back to haunt Mexico. “Remember,” she said, “nobody wins everything, and nobody loses forever.”

Ms. Sheinbaum is not inheriting an untroubled situation. Drug cartels have strengthened their hold over much of Mexico, and her first trip as president will be to the flood-stricken Pacific coast resort of Acapulco.

Ms. Sheinbaum must also deal with raging violence in the cartel-dominated northern city of Culiacan, where factional fighting within the Sinaloa cartel broke out in a feud between powerful drug kingpins.

Mr. Lopez Obrador has long sought to avoid confronting Mexico’s drug cartels and has openly appealed to the gangs to keep the peace among themselves, but the limitations of that strategy have become glaringly apparent in Culiacan, the capital of Sinaloa state, where gun battles have raged on the city’s streets.

Ms. Sheinbaum also inherits a huge budget deficit, unfinished construction projects and a burgeoning bill for her party’s cash hand-out programs —all of which could send financial markets tumbling. But perhaps her biggest looming concern is the possibility of a victory for Republican Donald Trump in the Nov. 5 U.S. presidential election.

The former president has already vowed to slap 100% tariffs on vehicles made in Mexico. Though that would likely violate the current U.S.-Mexico-Canada trade agreement, there are other things Mr. Trump could do to make life difficult for Ms. Sheinbaum, including his pledge of massive deportations.

Relations with Mexico’s northern neighbor were already tense after Mr. Lopez Obrador said he was putting relations with the U.S. embassy “on pause” after public criticism of the proposed judicial overhaul.

Jennifer Piscopo, professor of gender and politics at the Royal Holloway University of London who has studied Latin America for decades, said Mexico electing its first female leader is important because it will show girls they can do it too, but it can also create unrealistic expectations.

“Woman firsts are powerful symbols, but they do not gain magic power,” she said. “Especially when the governance challenges are so large, expecting magic solutions overnight can also generate outsized disappointment.”