Great story, great gameplay, great characters. What more could you want?
GAMEPLAY:
It's a turn-based RPG where you only control the main character, you use tactics to control the three other party members. The AI is very competent, although sometimes, they can do stupid things while you're slowly dying (I'm looking at you, Mitsuru).
The battle system makes the battles very quick, because it works on an element strength/weakness thing. However, where your enemies are weak or strong on something, you and your teammates are too. This could make the game really hard sometimes, because each time you or an enemy exploit a weakness or land a critical hit, they are granted "1 more" turn. When you die, your hours of training have been in vain and you have to restart from the last time you saved.
Also, this is a dungeon crawler mixed with an RPG mixed with a dating sim.
The dungeon crawler/RPG part comes when you're exploring Tartarus, a huge tower that has 250+ floors. You train here on the randomized floors. Because of the huge number of floors, this could make the game tiring, since it requires grinding.
The dating sim part comes when you're not exploring Tartarus. In this part, you interact with people to form bonds called social links, and those social links will help you in fusing personas.
Oh yeah, the main character is the only person capable of using multiple personas. To form new ones, there is a system called "Fusion" in which you combine from 2 to 6 personas to make a new one. There are around 170 possibilities, which makes the fusion system quite deep.
GRAPHICS:
This game has an anime style to it. The cutscenes are beautifully animated, the character designs are gorgeous and the personas are very detailed. The 3d graphics are kinda okay for the most part.
SOUND:
The music is J-pop, which is fine. Some tracks are awesome, but they're mostly used in boss fights and special events. The other times, however, they're reaaaaally repetitive, since you go to these places all the time. This is certainly the case for the music used while you're fighting, you'll be hearing this music throughout the game many, many, many times. The voice acting isn't bad too, some of the roles are very well played, while some others (Fuuka) sound emotionless. Fuuka sounds more emotionless than early Aigis. Aigis is a robot. Yeah.
STORY:
Oh my god, the story. The beginning is slow and linear, but after a while, it gets interesting. If you do not have a lot of patience, you'll probably quit soon enough. But if you are patient, you will be rewarded with a mature, deep, and immersive story with a satisfying climax (for some; and only if you get the good ending). I won't say anything about the story, because I've already said a lot of things already, and you should play it yourself.
Overall, a great game that could've been better if it had less grinding, a story that moves a little faster, and some less repetitive music. I hope someday that Atlus could make a remake, I would buy any console to have it.