Persona 3 - Social Link Guide
In Persona 3 you can form something called a Social Link by becoming friends with one of the many different ingame characters. When a Social Link is established the game notifies you by displaying the Persona archetype that the Social Link belongs to. Two of the very first Social Links you get in Persona 3 are the Fool and the Magician.
One could say that Social Links are essentially the Side Quests of Persona and as such they aren't required of you to do but are extremely helpful in making you more powerful throughout the game. Each time your friendship improves with someone in the game your corresponding Social Link will increase. For example, if you're hanging out with Kenji and you keep telling him to go for it and chase the woman he loves your Magician Social Link will improve.
Leveling up a Social Link will not grant you any active benefits for the Personas you already have made but each time you go to create a new Persona you'll gain experience for it depending on what level your Social Link is at.
Not all Social Links are available to you by default in the game like the Fool and the Magician are. Some of them you can only unlock at a certain time and some require higher than average Academics, Charm and Courage to unlock. For example in order to unlock the Moon Social Link you'll need at least "Unpolished Charm". If you're having trouble keeping up all your attributes and exploring Tartarus each night I strongly recommend you check out my guide on how to make the most of each day.
What Social Links should I raise?
If you are new to the game and especially the Persona universe you're probably wondering what Social Links are the ones most worth focusing on. Truthfully the best approach in Persona is to befriend as many people as possible as the first few ranks of each Social Link are usually super easy to get. Throughout the game you are going to be frequently switching Personas so the smartest thing to do for a beginner is try and cover as many Social Links as possible.
You of course can focus on a few Social Links too and primarily keep an eye out for Personas of that type. If you are a completionist I recommend that route over leaving a lot of Social Links half finished. The only reason for raising some of the SL but not maxing it is because you can create Persona's above your level if they gain that experience via your Social Link. What I mean is, if you are level 40 and you create a level 40 Persona that's tied to a level 10 Social Link of yours it will gain experience that puts it above your level and still be usable.
If you go the route of only maxing out a few Social Links; make sure you do a variety. Don't focus on Persona types that only perform magical attacks for example. You'll want to make sure your main character can play every role and swap between every role fluently. Sometimes the computer's AI is far too stupid and can't be relied on to win a battle for you or to exploit a monster's weakness.
Once you raise a Social Link to 10 you'll see it say the same thing as the picture above. This is the highest a Social Link can go and you won't gain any more benefit from spending time with that person. The best thing to do at this point is to find another Social Link to spend time on! If you'd like a list of all the Social Links and how to do them here's some links you may be interested in!
Fool
Magician
Priestess
Empress
Emperor
Hierophant
Lovers
Chariot
Justice
Hermit
Fortune
Strength
Hanged Man
Death
Temperance
Devil
Tower
Star
Moon
Sun
Judgment
Aeon