Social Links are a core mechanic in Persona 3 FES, representing your relationships with various characters. Each Social Link corresponds to an Arcana, and leveling them up grants bonus experience when fusing Personas of that same Arcana. Maxing out a Social Link allows you to fuse the ultimate Persona of that Arcana. To advance a Social Link, you typically need to spend time with the character, answer their questions correctly, and sometimes have specific Social Stats (Courage, Charm, Academics) at a certain level. Always carry a Persona of the matching Arcana when spending time with a Social Link to gain bonus relationship points. Prioritize the school-based Social Links as they are often time-limited.
