Malbus

Gonadore is the het ship between Albus Dumbledore and Minerva McGonagall from the Harry Potter fandom.

Canon
Dumbledore and McGonagall are very close friends and coworkers at Hogwarts. Prior to the events of Harry Potter and the Philosopher's Stone, Dumbledore (at the time her teacher) encouraged McGonagall to become an Animagus. McGonagall, after leaving school, took up a job at the Ministry of Magic, but found she did not enjoy it. She sent an owl to Hogwarts asking to teach there, to which she received a response hours later, offering her a job in the Transfiguration department, under Head of Department, Albus Dumbledore. Their friendship truly began when Dumbledore discovered McGonagall in tears in her classroom late that evening, and she confessed her family story to him.

Dumbledore offered both comfort and wisdom, and told McGonagall some of his own family history, previously unknown to her. The confidences exchanged that night between two intensely private and reserved characters were to form the basis of a lasting mutual esteem and friendship. Shortly after Dumbledore took the headmaster's position, he invited McGonagall to be the vice-headmistress. At some point during this time, they started addressing each other by their first names.

After Voldemort attempted to murder Harry Potter, Dumbledore sent McGonagall to watch the Dursleys. They meet up later that night to discuss Harry's future. She disagreed with Dumbledore putting Harry in their care, but eventually agreed it would have to do. He also entrusted McGonagall, as well as several other teachers, to put up defences to protect the Philosopher's Stone.

Before the beginning of the Chamber of Secrets, Dumbledore hired Gilderoy Lockhart as a Defence Against the Dark Arts teacher, to which McGonagall asked what the students could possibly learn from "a man as vain and celebrity-hungry as Lockhart".

During the events of the Goblet of Fire, McGonagall and Dumbledore disagree on whether to remove Harry from the Triwizard Tournament. During the Yule Ball, they waltz together. After Cedric Diggory's death, they notice that Harry is gone, as is Alastor "Mad-Eye" Moody. They, alongside Severus Snape, overpower Moody (revealed to be Barty Crouch Jnr).

After Cornelius Fudge refused to believe Voldemort had returned, McGonagall firmly stood beside Dumbledore. McGonagall and Dumbledore both mutually dislike Umbridge but neither clash heads with her. When Cornelius Fudge attempted to arrest Dumbledore alongside many Aurors, McGonagall stepped forward and announced her intention to fight the Aurors on his behalf. She only stepped back at Dumbledore's insistence when he reminded her that Hogwarts and her students would need her in his absence.

McGonagall was devastated when Dumbledore was killed in 1997 during the Battle of the Astronomy Tower and attended his funeral. Even after his death, she trusted his opinion and stood beside Harry, knowing it was part of Dumbledore's plan. After Snape died, she took up the role of headmistress.

Fanon
Prior to J.K. Rowling revealing Dumbledore is gay, Gonadore was not among the popular ships in the Harry Potter fandom. Fantastic Beasts and Where to Find Them set the ship apart due to conflicting sexualities.

However despite this there are still those who ship them. The ship is also quite popular as a friendship, more so than as a romantic pairing.

Fandom
Albus Dumbledore/Minerva McGonagall on A03

Albus Dumbledore and Minerva McGonagall on FanFiction.net

Dumbledore x McGonagall tag on Wattpad

Trivia

 * McGonagall became an Animagus thanks to the encouragement of Dumbledore.
 * Both McGonagall and Dumbledore were in Gryffindor.