I went looking for the troll because I -- I thought I could deal with it on my own -- you know, because I've read all about them.
-- Hermione Granger, lying her head off (PS10)
The mountain troll is very stupid. It stands twelve feet tall, with grey skin, a lumpy body, and flat horny feet. It exudes a powerfully awful smell, “a mixture of old socks and the kind of public toilet no one seems to clean.” Its nose is full of what looks like lumpy, gray glue: troll boogers (PS10).
Quirrell, to create a diversion so he could go after the Philosopher's Stone, let a mountain troll into the castle on Hallowe'en, 1991. It wandered around the corridors until Harry and Ron locked it in a girls' bathroom. Right after they did that, they realized that Hermione Granger was in that particular bathroom, and they had no choice but to charge in after it. With a lucky combination of derring-do, desperate magic, and sheer dumb luck, they managed to knock it out and save Hermione (PS10).
Pierre Bonaccord, the first Supreme Mugwump of the International Confederation of Wizards, wanted to stop troll-hunting and give them rights, but his appointment to that office was contested by Liechtenstein, since they were having problems with a tribe of very dangerous mountain trolls at the time (OP31).
Mountain trolls have been known to ride Graphorns, or at least try to ride them. Graphorns don't seem to be very keen on the idea, and it is less common to see a troll riding and Graphorn and more common to see a troll covered in Graphorn scars (FB).