These are all the social links avaliable to you during the game. Below will tell you information on how to obtain them and their attribute and what Personas you can make more powerful by obtaining the social link!
0. The Fool
The SEES Group Social link. You obtain this automatically.
Personas: Orpheus, Legion, Ose, Black Frost, Decarabia, Loki, Susano-O
I. The Magician
Kenji, one of your classmates, is the one you'll build a bond with in this social link. He is usually found in your classroom on the weekdays. Not all, but most.
Personas: Nekomata, Jack Frost, Pyro Jack, Sati, Orobas, Ranga, Surt
This social link is made with Fuuka. You'll need max courage in order to go out with her. [This is one of the girlfriends in the game.] When she is avaliable to go out, she'll be standing in the hallway that your classroom is located on, near the stairway going down to the lobby.
Personas: Asparas, Unicorn, Sarasvati, Ganga, Parvati, Kikuri-Hime, Scathach
This social link is forged with the Student Council President, Mitsuru. You'll need to max your Academics to go out with her. When she is avaliable, you can meet her by the Faculity room in the first floor hallway.
Personas: Lakshmi, Hariti, Gabriel, Mother Harlot, Skadi, Alilat
This social link is with Hidetoshi from the student Council. You'll need to join the Student Council whenever Mitsuru asks you to. Remember, the only days you can increase the social link is on the days the Student Council meets. This would be Mondays, Wednesdays, and Fridays.
Personas: Forneus, Oberon, Take-Mikazuchi, King Frost, Raja Naga, Kingu,
Mitsuko and Bunkinchi, the old couple from the Bookstore is the ones you'll bond with. When the bookstore reopens you can talk to them and they'll talk to you about a tree planted at the school. Go back to the school and get the left by the large tree in the courtyard. Take it back to couple and the link will be formed! You can increase it on any day, minus Sundays and Holidays.
Personas: Omoikane, Berith, Flauros, Beiji Weng, Ananta, Daisoujou, Huang-Long
Yukari is the one you'll bond with. To get this you'll need to max your charm. She stands in the back of the classroom on the days you can go out with her.
Personas: Pixie, Narcissus, Queen Mab, Saki Mitama, Titania, Raphael, Qubele
Kazushi is also a member of the sports team you choose. You can meet him in your classroom whenever he is avaliable to go to the club meets.
Personas: Ara Mitama, Chimera, Ares, Omitsunu, Nezha, Komokuten, Thor
Yuko, the manager of the sports team of your choice. You'll need the Level 3 Chariot link to hang out with her. You can only date her on Wednesdays and Saturdays.
Personas: Valkyrie, Titan, Jikokuten, Hanuman, Nrisinha, Kali, Siegfried
Maya, the online personality, will be the one you bond with here. You'll hang out with her by playing the online game that Junpei gives to you early on. You can only forge this social link on days off from school.
Personas: Yomotsu-Shikome, Naga, Lamia, Taraka, Kurama-Tengu, Nebiros,
You'll bond with Keisuke, a member of an "art" club of your picking. He can hang out on days the club meets, or rather, Tuesdays, Wednesdays, and Thursdays.
Personas: Fortuna, Kushimitana, Clotho, Lachesis, Atropos, Norn
Shy Chihiro will be the one you'll spend quality time with. She's shy at first, so you'll need to get her to warm up to you. After you do, she can spend time with you.
Personas: Angel, Archangel, Principality, Power, Virtue, Dominion, Throne,
XII. Hanged Man
Little Maiko, at the shrine, is the cute little girl in this link. She'll ask for Mad Bull and Takoyaki. You can play with her everyday but Sunday.
Personas: Inugami, Take-Minakata, Orthrus, Vasuki, Ubelluris, Attis
This is with Pharaos and will happen automatically.
Personas: Loa, Pale Rider, Samael, Mot, Alice, Thanatos
This is with Bebe. Can only forge this one on 6/5 at the home ec room if you are of Average Academics. He'll stand outside the classroom when you can hang out with him.
Personas: Mitra, Genbu, Seiryuu, Okuninushi, Suzaku, Byakko
President Tanaka, the popular home-shopping personality is who you'll spend some... uh... "quality" time with. Hermit social link needs to be level 4. When it is, you can meet him at the Port Island Station anytime Saturday through Tuesday.
Personas: Lilim, Vetala, Incubus, Succubus, Lilith, Abaddon, Beelzebub
The Strength Social link needs to be level 5. On Thursdays-Sundays you can find him at Club Escapade. He'll be the man up the stairs at the top. This link is with Mutatsu.
Personas: Cu Chulainn, Uriel, Bishamonten, Wu-Kong, Masakado, Shiva, Chi-You
This is with Mamoru. Need the Level 4 Courage Social Link. You'll find him at the station on any given day sitting on a bench.
Personas: Nandi, Kaiwan, Ganesha, Garuda, Saturnus, Lucifer
This is with Nozomi. Need to have the Level 4 Magician social link. He'll be sitting on a bench in the mall. He's a chubby little fellow. You'll have to answer all his questions correctly, and he is there everyday but Sunday/Holidays.
Personas: Gurr, Yamata-no-Orochi, Grimehkala, Dinoysus, Chernobog
XIX. The Sun
Akinari is who you'll bond with. You'll need to have a social link with the Hanged Man first. He'll appear on Sundays at the shrine. He'll say something about his pen missing. When you go back to the dorm, her his pen from Koromaru. The next Sunday you can forge the bond, as he only appears on Sundays.
Personas: Quetzalcoatl, Jatayu, Horus, Metatron, Vishnu, Asura
Automatically happens towards the end of the game.
Personas: Anubis, Michael, Satan, Messiah
Aeon - FES ONLY
The Aeon Social Link is unique to Persona 3: FES. This social link features Aegis. The social link can be initiated after Aegis is repaired, late in the game.