You take the role of Vayne, an orphan with inexplicably strong alchemic powers. His powers earn him the attention of the Al-Revis Alchemic Academy, which is the alchemic equivalent of Hogwarts' School. Most of the gameplay follows the same semester-based structure; after signing up for a class, you complete assignments. Assignments involve everything from collecting the necessary items to complete an item to killing a specific monster. Each assignment focuses on a specific gameplay element that comes in handy once you get the chance to explore on your own.
Although most classes feel like glorified tutorials at times, it is still important to complete them as best as you can. Each assignment is graded as a class. If you get a good grade, you are rewarded with "Free Time" to do whatever you want; fail and you'll have to redo the assignment. You really want to gain as much Free Time as you can since it allows you time to go out and meet party members as well as learning new skills that you probably wouldn't learn in class. Make-up assignments are also typically more challenging than your original assignment.
The entire structure feels a lot like Persona 3, though it isn't as compelling. The school-based structure is fine, though it lacks the same sense of "openness" as Persona 3's system. You'll meet plenty of characters and have a few cool adventures, but you never feel like you're building relationships with anyone. Everything feels a little too linear and structured, which makes some aspects feel forced, rather than giving you the freedom to play around. The structure also takes away from the feeling of progression. You're always returning to campus, which places limits on where you can go. True, Persona 3 faced a similar problem, but the number of things you could do, like chasing after the head cheerleader or joining a club, made the school feel like a setting, whereas Mana Khemia basically turns it into a structured dungeon.