A very solid game.
I wasn't sure about this game when I began playing it, but, as it turned out, I had a lot of fun with it. The art was perfectly done, the gameplay fun and interesting, and the BGM appropriate and fitting. Overall, a very solid and professionally done game.
There were a lot of little things that could have been improved upon in this. The first would be the tutorial. It was not very helpful. I went through my first game without even realizing I could upgrade my students, make them take a test, and pick their class. Once I found that out I had a lot easier time with the game - and a lot more fun :). Also, the whole "organize student" button could have been renamed into something more appropriate, like "grade student", or something that would differentiate it from organizing the student into a group.
Another thing that could have been improved upon was the battle system. While simple, it was very, very basic. There could have been a few more tactical options, spells, and fighting techniques offered to spice it up the action a bit, than just clicking on the enemy. The background for the hunts/arena were also very basic. Snow scenes, desert scenes, water scenes, ect, would added a little more interest to the game than just the standard field and arena scenes. The character AI needs some work to. When character stand idly by, a few feat away from an enemy, and you don't have that assistance feature turned off. The character also easily get stuck against obstacles - and this stuff makes it looks like bad programing.
The limited selection of quest was a bit of a disappointment. Lack of boss battle, a large plethora of enemy to fight, and actual dungeon spelunking were a few thing I would have liked to seen. Also, maybe, like others have suggested, adding teachers, and improving royal tournament times. Maybe even add exchange students who who try to sabotage your university, or something.
Other minor stuff would be the generic character portraits, and some of the character voices durring battles - like when you get male voices with an all female group, it sorta doesn't make much sense.:D
Other than that, good job on the game. If there a sequel in the works for this I'll look forward to playing it.