Toshinori Yagi/Relationships

Izuku Midoriya
At their first meeting, All Might thought that Izuku was just a fan, but he started to acknowledge him when he jumped to save Katsuki from the Hedoro Villain. From that moment, he was touched by Izuku's bravery (despite not having a Quirk) and decided he would pass his powers to Izuku, feeling that he is the only one worthy enough to inherit his strength, and they started to share a feeling of mutual respect for each other. He himself even mentioned that he has no regrets passing One For All to Izuku.

He's started to open up to Izuku as he sees his growth, going as far as to reveal personal details about his past such as how he was Quirkless, his fight with All For One. He continues to express his pride in his growth as a hero.

Upon Sir's prediction of All Might's death soon, All Might accepted this prediction openly but he states that Izuku's will and growth, constantly surpassing his expectations gives him the desire and reason to live long to see his successor become the hero he wishes to be.

Shota Aizawa
Not much is known of their past, but due to their contrasting personalities, they do not get along very well, with Shota disliking heroes that lap up the media spotlight being a major point of contention. Toshinori and Shota also frequently disagree with teaching methods, with Toshinori criticizing Shota's harsher attitude towards their students. Neverless the two do show mutual respect for each other and their abilities, and both being willing to risk their personal safety to protect the other such as in the Unforseen Simulation Joint Arc. Over the course of the series, Shota and All Might's relationship appears to have gotten a little better, particularly after All Might's retirement. Shota counseled with All Might regarding their job to have students enter the dormitories. The two also offered to buy each other a drink, indicating they are both willing to socialize together casually.

Chiyo Shuzenji
Chiyo is one of All Might's friends that knows about his condition and his Quirk. She frequently scolds him for letting Izuku damage himself in fights and for not being a good enough mentor.

Nedzu
Nedzu is another of the few people that knows of his condition and was the person that offered him a teaching position at U.A..

Naomasa Tsukauchi
Naomasa is also another person that knows about his condition; All Might thinks he is the best cop there is.

Enji Todoroki
Ten years before the start of the series, All Might once had a talk with Enji and since then, they have not spoken to each other. All Might appears to respect Enji, wanting advice from him on how to raise the next generation. It seems that their rivalry is mainly one-sided (on Enji's) as All Might is usually friendly with him.

Katsuki Bakugo
All Might acknowledges Katsuki as a promising hero. However, he does not approve of his reckless and cruel fighting style, as he greatly scolded the boy for using an attack on Izuku that could have killed him. He often tries to give him advice which usually falls on deaf ears due to Katsuki's anger.

Gran Torino
Gran Torino trained All Might back when he was a student. Though he respects his mentor, All Might is somewhat skittish about talking about him to Izuku due to past trauma from his training methods.

Nana Shimura
Nana Shimura was All Might's mentor and his predecessor, the 7th inheritor of the One for All quirk. Nana was the one that told All Might that a true hero should smile no matter what, to reassure the people and to not only protect their lives but also their hearts. All Might greatly respected her as a mentor, friend and hero; All Might became enraged when All For One badmouthed her.

All For One
All Might and All For One are bitter enemies and detest each other; All Might despises All For One's antagonistic and manipulative nature while All For One despises All Might's heroism. All Might fought All for One five years ago and defeated him, which furthered All For One's hatred for All Might. All For One is an incredibly powerful villain and gave All Might his critical wounds that limit his ability to perform his duties as a Hero. All Might is very cautious about All for One, going as far as to warn Izuku of the dangers that he poses. He seems to also place his hand on the wound All for One dealt him when talking about him.

Noumu
Noumu was a creature, specifically created to kill him. All Might became aware of how dangerous he was personally, after fighting him in the Unforeseen Situation Joint. After a short but brutal fight, All Might managed to defeat and capture Noumu, but was severely injured and exhausted from the fight.

Toxic Chainsaw
While they have yet to be seen interacting, All-Might likely holds a grudge against Toxic for scaring him,

Sir Nighteye
Sir Nighteye was once All Might's sidekick before their eventual falling out. All Might is reluctant to meet his old sidekick again due to becoming something Nighteye warned him about.

Mirio Togata
Before meeting Izuku, Principal Nedzu suggested Mirio to be All Might's successor.