Who is the teacher in the school Harry is going?

Professor McGonagall

Minerva McGonagall is the Transfiguration professor and head of Gryffindor House. She is also an animagus, possessing the ability to turn herself into a tabby cat. Professor McGonagall is present when Professor Dumbledore leaves Harry on the Dursley's doorstep and strongly opposes his decision to leave Harry with such an unpleasant Muggle family. Although Professor McGonagall is known for being strict, even with the members of her own house, she has a particular fondness for Harry, especially when she sees his spectacular dive for Neville's Remembrall and recruits him for the Gryffindor Quidditch team.

In the attempt to protect the Sorcerer's Stone from Voldemort, Professor McGonagall creates the challenge with the giant chess set.

Professor Snape

Severus Snape is the Potions master at Hogwarts. A former student of Slytherin, Professor Snape is now head of Slytherin House and shows clear favoritism to its members, particularly Draco Malfoy. Harry instantly dislikes Professor Snape and soon learns that his father and Snape were classmates who despised each other. After learning that Fluffy is guarding the Sorcerer's Stone, Harry immediately concludes that Professor Snape is the one who is attempting to steal it in order to bring Voldemort back to power. This conclusion is supported when Hermione sees Professor Snape appearing to hex Harry's broom during a Quidditch match (in actuality, Professor Snape was attempting a counter-curse to overcome Professor Quirrell's hex). Despite his attempt to save Harry, Professor Snape maintains his antagonistic view of Harry and the two remain at odds until the very end of the series.

In the attempt to protect the Sorcerer's Stone from Voldemort, Professor Snape creates the challenge with the riddle of the seven potions.

Professor Quirrell

Quirinus Quirrell is the Defense Against the Dark Arts professor at Hogwarts. Harry first meets Professor Quirrell at the Leaky Cauldron during his first visit to Diagon Alley and is struck by Quirrell's stammer and nervousness. After working as professor of Muggles Studies at Hogwarts, Professor Quirrell took a year-long sabbatical during which, according to rumors, he had a confrontation with Albanian vampires. In actuality, Professor Quirrell encountered Voldemort and became seduced by the power of the Dark Arts. While at Hogwarts, his nervous appearence is only a cover while he attempts to steal the Sorcerer's Stone and bring Voldemort back to power. In the meantime, Quirrell keeps Voldemort alive by sneaking into the Forbidden Forest and drinking unicorn blood. Although Harry only discovers Professor Quirrell's true nature at the end of the book, Professor Snape is aware of Quirrell's treachery almost immediately and attempts to keep Quirrell from hurting Harry and finding the Stone.

In the attempt to protect the Sorcerer's Stone from Voldemort, Professor Quirrell creates the challenge with the troll.