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'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.

Shouta Aizawa
Not much is known of their past, but due to their contrasting personalities, they do not get along very well.

Chiyo Shuuzenji
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 Yuuei.

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 Bakugou
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.

Sensei
All Might fought Sensei several years ago. Sensei 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 Sensei, going as far as to warn Izuku of the dangers that Sensei poses. He seems to also place his hand on the wound Sensei dealt him when talking about him.