* Al-Azhar is world seat of Sunni Islamic learning
* Brotherhood seeks to make al-Azhar hub of dissent
* Campus protests worry army-backed government
By Maggie Fick
CAIRO, Dec 20 (Reuters) - A venerable centre of Islamic learning in Cairo has become a new battlefield in the Muslim Brotherhood's struggle to keep its battered cause alive against Egypt's army-backed rulers.
When General Abdel Fattah al-Sisi appeared on television in July to tell Egyptians he had deposed their first freely elected leader, the grand imam of al-Azhar was among those at his side.
Sheikh Ahmed el-Tayeb, who looked on as the army chief of staff promised new elections, was falling in with al-Azhar's decades-long practice of lending its prestige to those in power.
But Tayeb now faces a maelstrom of unrest at al-Azhar's main campus in Cairo, where students are demanding the reinstatement of President Mohamed Mursi, a Brotherhood leader.
"We find it dishonourable to have a grand imam who supports a bloody military coup," said Youssef Salahein, 21, an undergraduate in Islamic studies and English.
"We are not going to stop until he is out of al-Azhar and he is judged for his crimes alongside all the military leaders."
The anger on the once-tranquil campus contrasts with the pro-Sisi mood elsewhere in Egypt, where the Brotherhood has failed to mobilise widespread support via street protests.
Instead its cadres, vilified as terrorists by the media and the state, are once again in jail or underground, after leading the movement to one electoral triumph after another following the popular unrest that felled President Hosni Mubarak in 2011.
Now the bloodied Brotherhood appears to see al-Azhar as a potential weak point for the government, which like most of its predecessors is determined to ensure that Islamists do not use religious institutions to rally support against their rule.
Tayeb and Sisi remain allies, but pro-Brotherhood feeling among students and faculty at al-Azhar, whose renown spans the Sunni Muslim world, has put the government on the defensive.
HUB OF REBELLION
Entrenching dissent at al-Azhar would enable the Brotherhood to deprive the government of the Islamic credentials with which the institution cloaked Egypt's military rulers for six decades.
Beyond the campus, the authorities have tightened their grip since Mursi's ouster, violently dispersing Brotherhood rallies, outlawing the Islamist movement and arresting its leaders.
Rights groups say more than 1,000 Mursi supporters have been killed in the worst internal violence in Egypt's modern history.
As in Mubarak's era, the religious endowments ministry vets sermons and has shut down some small neighbourhood mosques where independent imams lead prayers. In November, a new law banned protests at places of worship.
The pressure has prevented the Brotherhood from keeping up mass street protests, but has not stopped the ferment at al-Azhar, whose campus lies near the military parade ground where Islamic militants assassinated President Anwar Sadat in 1981.
Students have spray-painted buildings, blocked college entrances and staged strikes, prompting the university president to request police intervention last month - fuelling the wrath of students and professors who say the campus is a sacred space.
Some professors who silently sympathised with the Brotherhood but never dared criticise al-Azhar's leadership in the past are now speaking out.
"In the end these students are the responsibility of Sheikh el-Tayeb and he should protect them," said Reda Ahmed, 38, a professor who was shot in the groin during an attack by security forces on Mursi supporters in July.
Despite the risks, more professors are quietly voicing support for the students, giving the Brotherhood political ammunition it can't seem to find outside the campus walls.
"I can't participate, but I'm with them in my heart," said a professor who asked not to be named for fear of reprisals.
He estimated that 80 percent of the faculty in his college were pro-Brotherhood, but said most feared arrest if they made their views public - Islamist-leaning professors say undercover state security agents attend and record their lectures.
Last month a court jailed 12 al-Azhar students for 17 years after they took part in demonstrations. Security sources say 88 students are still in detention after fierce clashes last week.
The campus reveals signs of rage against the government before January's referendum on a constitution that strengthens the army's hand and bans religious political parties.
Graffiti underscores a deep disdain for Sisi, and for the man who sat next to him when the army takeover was announced.
"(Sheikh) el-Tayeb is Sisi's dog," read graffiti in a courtyard. "Uprising of al-Azhar" is another tagline.
Nevertheless, not everyone at al-Azhar favours the student agitation in support of the Brotherhood.
"This is chaos," said Amna Nusseir, 70, a professor of Islamic Studies and Arabic who also sat on the committee that drafted the new constitution. "They (Brotherhood members) are liars, they don't feel shame. I hate them for this."
On one afternoon this month, about 100 women students at al-Azhar chanted slogans against "military rule" on a busy street outside their dormitory complex, snarling traffic.
Some students complained that the daily disturbances were disrupting their studies. Summing up the mayhem, one said: "We have exams, but we don't have lectures." (Editing by Michael Georgy and Alistair Lyon)