CHICAGO — Lori Lightfoot, a political novice, swept into Chicago’s City Hall in staggering style, winning 73 percent of the vote and sending a deafening message to the political veteran she had defeated. She pronounced the results a “broad mandate for change.” She promised to break the city’s endless cycle of corruption. She pledged to remake Chicago.

“Thriving, prosperous, better, stronger, fairer — for everyone,” Ms. Lightfoot said, beaming from a microphone in the hours after the votes were cast.

But this is Chicago, a city that is vast, complex, set in its ways and full of problems that are now Ms. Lightfoot’s to solve.

Ms. Lightfoot, who will become this city’s first black woman mayor and its first openly gay mayor when she takes office in May, made clean government a centerpiece of her agenda. But Chicago still carries the vestiges of its notorious political machine and, by some measures, more corruption than any other American city. Chicago’s entrenched and decades-long struggles with crime, segregation, policing and inequity loom. And its longstanding fiscal problems are urgent: Ms. Lightfoot must come up with another $1 billion to deal with a looming pension crisis, and fast.