They have been waiting for two and half years and the children of Iraq's east Mosul are flocking to enrol in their reopened schools, eager not to waste another day.

"It's a great day, today we are giving our children their right to receive an education," said Ghassan Ahmed, queueing with his seven-year-old in the yard of Farahedi primary school.

The red-and-yellow walls of the school in Muharbeen, a neighbourhood of northeastern Mosul that was retaken from the Islamic State jihadist group, are still riddled with bullet holes.

Life is starting to return to the city's east bank, which Iraqi forces have now completely retaken from IS, 100 days into a vast military operation launched in mid-October on the jihadists' last major stronghold in the country.

Ghassan Ahmed was a professor at the University of Mosul before IS seized the city in June 2014.

Like many other parents, he refused to send his child to school under IS's self-proclaimed "caliphate". His son has never been to any school.

"I kept them at home and started teaching them the official curriculum of the Iraqi government myself," he said.

Across the street, the charred carcass of a building stands as a reminder that only days ago the entire neighbourhood was a battlefield where jihadists countered advancing Iraqi forces with suicide car bombs, snipers and mortar fire.

Mohammed, a nine-year-old from the neighbourhood, said IS burnt down the house as part of tactics to prevent raids by US and other warplanes on their positions.

- 'Education cannot wait' -

Just like 250 other children, Mohammed was at the Farahedi school for the first time since the jihadists took over his city.

He said he could not wait to return to school despite the fact that it still lacked running water, electricity and schoolbooks.

"I'm super happy to be going back to class. I want to become a doctor," he said with a toothy grin.

As an explosion rumbled in the distance, the birds fell briefly silent but Mohammed didn't flinch and went off to play with his friends.

In east Mosul, which a minority fled when the offensive was launched but where half a million residents stayed, 30 schools reopened this week and a total of 16,000 children were enrolled.

"Education can't wait. It must be a priority," Maulid Warfa, who heads the UN children's agency UNICEF in Arbil, the nearby capital of Iraq's autonomous Kurdish region, told AFP.

"Schools can be a tool to slowly help them heal from the trauma... Many children in this city have seen way too much destruction and death."

According to the Britain-based charity Save The Children, at least 300,000 children live on Mosul's west bank, which is still fully controlled by IS and expected to see bitter street fighting in the weeks ahead.

Millions of children have lived under the tyrannical rule of IS since the group proclaimed its caliphate in June 2014.

Many were kept out of school for more than two years, some forcibly enlisted as child soldiers.

- Building the future -

The jihadist group has lost about two-thirds of the territory it once controlled in Iraq, but its trademark ultraviolence has traumatised the population.

The immediate challenge, however, is to bring children back to school, UNICEF's Warfa said.

"With two million inhabitants in Mosul, bearing in mind that 35 percent of the population are children, we're really talking about a huge number of children who will need to go back to school," he said.

"It's a huge task," said Warfa, adding that another 40 schools were scheduled to reopen in coming weeks.

In Zuhoor, another neighbourhood of northeast Mosul, Haider Adnan is one of the oldest returning pupils to stand in line behind the headmaster's desk with his enrolment form in hand.

At 18, he said he wanted to complete his secondary education before signing up for university and hoped to learn about "history, geography and real religion".

Haider was one of a minority who attended the schools run by IS, whose teachers he said spent most of their time extolling the lives and achievements of the group's supremo Abu Bakr al-Baghdadi and other jihadist figures.

"History is important because it is the life of our forefathers -- how they lived and they evolved," he said. "It becomes a lesson that teaches us how to build our own future."