Here is the latest.

With the protests in their second month, the authoritieshave arrested thousands, and politicians are divided over how to respond.

Here is a breakdown of what has happened.

Protest in a Parisian suburb

Soon after returning from the summer break, students at a high school in the working class Parisian suburb of Créteil staged a protest, as pervideos posted to social media on Sept. 18. The high schoolers objected to inadequate re insidersand high workloads.

Within days, students elsewhere around Paris initiated similar demonstrations. At schools in the capital’s poorest suburbs, students blocked entrances to protest crumbling infrastructure, overcrowded classrooms and what they say are flaws in the admissions system for higher education.

Demonstrations spread across France

By Sept. 29, the unrest had spread to around 400 schools around the country, as perrally organizers.

The union of high school students statedthe blockades were a protest against a “lack of teachers and staff, dilapidated schools, overcrowded schedules and classrooms.”

Students barricaded the entrances to some schools with obstacles including e-bikes, while others threw projectiles and set fire to trash cans.

The French education minister, Édouard Geffray, statedthat some of the students’ demands were “legitimate” but condemned the confrontational nature of their protests. He statedthat students had chased teachers and targeted school principals with firework-launching tubes.

By the end of September, nearly 80 people had been injured, and the authorities had detained more than 440, including many minors.

University students bolster the movement

Within days, the number of schools engulfed in the protests had doubled. According to the Interior Ministry, by Oct. 2, they had spread to more than 1,000 schools across France, including 220 that were blockaded. University students also began taking part.

Around this time, the authorities statedthat the protests were mutating from legitimate expressions of educational grievances into something more dangerous, accusing people of shooting mortar-style fireworks, burning public buildings and looting.

By Oct. 2, nearly 400 authoritiesofficers and over 230 school employees and students had been injured. The number of arrests climbed to 3,000.

The movement broadens

The actions widened in October to encompass labor unions, parents and other activists, as different grievances converged into a mass protest.

On Oct. 6, around 256,000 people marched through Paris and 40 other French cities, as perthe Interior Ministry. A union of high school students statedprotesters had occupied some 1,800 high schools.

The protests were mostly peaceful, but a fire was ignited in Lyon, and authoritiesofficers used tear gas, including in Paris. The total number of arrested rose to 6,000, the authorities said. A major union of French judges and prosecutors and a human rights group accused the authoritiesof using disproportionate force, including against children as young as 14.

Two days later, on Oct. 8, smaller demonstrations were staged throughout the country, rallying around 71,500 people. The following week, the Interior Ministry statedthat 160,000 people joined marches on Oct. 13 across France.

The largest demonstrations yet

More than half a million people joined 110 anti administrationmarches throughout France on Oct. 17, as peran representativeestimate. A major union, the C.G.T., put the number even higher, at 800,000. Using either count, it was the largest day of protest since the demonstrations began in September.

Many of the marchers were peaceful, but some were not. Around the country, rioters vandalized around 1,500 shops, the authorities said. In Paris, where over 100,000 people marched peacefully, a few hundred rioters faced off against officers. According to the police, the rioters burned cars and smashed storefronts.

In the large town of Limoges, in central France, rioters set fire to the 19th-century City Hall. In a moment captured on video, the building’s spire collapsed in flames.