The first is The Fool, which represents the SEES Social Link between you and everyone that lives in the dorm.
The Social Link goes up a level every time you and the party defeat a boss representing the major Arcana.
She later joins the party in battle, with Fuuka Yamagishi replacing her as the permanent support for the rest of the game.
Mitsuru is the president of student council in Gekkoukan High School, as well as the school's senior valedictorian.
Some of them are a little more difficult to begin, oftentimes involving talking to the same character more than once for a certain number of days to begin the Link, or obtaining a certain level in Academics, Courage, or Charm.