Greek Mythology found in Harry Potter's Sorcerer's Stone

Fluffy is like Cerberus. They both have multiple heads and can be put to sleep easily by the sound of music. In Greek mythology, Orpheus used a harp to pass the cerberus into the underworld. Similarly, Professor Quirrell used a harp to pass Cerberus to go down and "under" the trap door.

Argus Filch, the caretaker, can be compared to the mythological monster Argus. Argus has a hundred eyes. Although Filch definitely does not have a hundred eyes, he is always watching out for any trouble so that he can immediately punish the student, which could symbolically be similar to having a hundred eyes.

In Greek mythology, Hermione was the name of the daughter of Menelaus and Helen. 

Harry is equivalent to any myth that has a hero; Harry would be the hero of the story. In my opinion, I think Harry is similar to Achilles in that he's a strong "warrior" and very brave.

Professor McGonagall's first name is Minerva which is the Roman name for the goddess Athena. Athena is the goddess of wisdom and McGonagall is known for being very wise and tactical.

There are centaurs in greek mythology and in Harry Potter. They are half man and half horse.

Hermes is the name of Percy's owl. It is named after the Greek god messenger Hermes. Owls also send messages in the wizarding world as well.

Hogwarts has similarities to Mt. Olympus where the gods and goddesses lived. It was a high mountain that couldn't be accessed by the human world. Hogwarts also cannot not be reached by humans and is inhabited by the wizards who are also not human like the gods.