Mont-Royal (Mount Royal) is the mountainous (okay, very hilly) park situated a little south of the centre of Montreal. It was planned by Frederick Law Olmsted, the designer of Central Park in New York City and the grounds of the U. S. Capitol. It's the largest park on the island. The two most striking features of the park are the lookout, which has a wicked view of downtown, and the giant illuminated cross on top of the mountain. The cross is outfitted with two sets of light bulbs: usually, the white bulbs are the only ones which are used. However, whenever a Pope dies, the white bulbs are switched off and a second, purple set are illuminated (giving Montreal the distinction of having the world's largest, if not only, Pope-o-Meter).
A good portion of the mountain is taken up by four cemeteries: Cimetiere Notre-Dame-des-Neiges (home of the infamous F U C K Y O U-acrostic tombstone), Mount Royal Cemetery, Shaar Hashomayin Cemetery, and the Spanish and Portugese Cemetery. If you're not creeped out by graveyards, these are really nice places to chill in (although I haven't been back since I got lost in Notre-Dame-des-Neiges at 2 in the morning).
The rest of the park is more typically park-like: there are bike paths, a staircase to the top of the mountain, a lake, a chateau, and so forth. McGill University borders the south-east edge of the park; Universite de Montreal sits on the north-west corner. On the eastern edge of the park is the George-Etienne Cartier monument, home of the Tam Tams.
Mount Royal is not an extinct volcano; it is a gabbritic extrusion. This is the one thing that I remember from geology class.