I got help from 'MrTommo2304's video where he summarises the complete story of Bleach up to TYBW. This will be the only chapter that is this heavily summarised though.
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In the town of Karakura, there lives an almost average boy by the name of Ichigo Kurosaki. With his twin sisters Karin and Yuzu and their loving and overbearing father Isshin.
When he was younger, Ichigo considered his mother to be the centre of his world, always smiling when he was with her and regularly holding her hand. She always seemed to know what to say to make him happy again.
At a very young age, Ichigo heard his father saying his name means "to protect one thing," which instilled in him a desire to protect his mother. When his sisters were born, he began attending a dojo for the sake of protecting them.
This will, to protect seems to be his purpose. It is what drives him and defines him. His name was perfectly chosen.
As a teenager, Ichigo is stubborn, short-tempered, strong-willed, and impulsive. Despite claiming not to care about what other people think about him, he attempts to maintain a detached and "cool" image. He generally keeps his face set in a near-permanent scowl, with his eyebrows drawn together.
His outspoken, hot-headed demeanour is a trait Ichigo himself has acknowledged, and if somebody picks a fight with him, he cannot help fighting back.
And he seemingly gets into fights often, due to his orange hair that many seem to make fun of.
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Despite seemingly being a normal teenager of 15 years of age, there is something unusual, however. He can see ghosts.
Invisible to normal humans, these ghosts come in different forms, from the friendly and often timid ones that Ichigo knows of, to ... well less friendly ones.
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One night a mysterious woman, clad in a black outfit steps through the wall into Ichigo's bedroom.
Due to Ichigo's ability to see spirits, he spots this woman, whom he already encountered the other day.
The woman grabs her sword and Ichigo seemingly panics.
"Who are you?! What do you want?"
The woman doesn't answer him however and just looks around the room.
"Hey!", he says.
"It's near...", the woman says. However, she is then kicked in the back by Ichigo who is angry at this point.
"What are you talking about, idiot?! First, you scare the living daylights out of me, then you ignore me? I'm asking who you are!"
The woman turns around surprised and asks him.
"Y-you ... you can see me? But wait ... you just kicked me..."
"Huh? What are you babbling about? Of course, I can see you."
The woman stands up and looks at Ichigo.
"You were the one in town earlier, weren't you?"
"You just noticed?", he asks her.
"Strange ... People usually can't see me ..."
"Quit talking nonsense ..."
"Alright, I will tell you ... I am ... a Shinigami."
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After that, the woman tells Ichigo what she is and where she comes from.
"I see. So you're a Shinigami ... And you've come all the way here from this Soul Society place in order to exorcise evil spirits. So that means that the monster was an evil spirit ... and it attacked that girl.
Okay, I'll believe you ... Idiot! Do you think I'd believe that?!"
Ichigo and the female Shinigami have a little disagreement because Ichigo does not believe her story at all. He finds it hard to believe and who could blame him?
That is until the Shinigami performs Soul Burial and sends a plus that is inside Ichigo's room to Soul Society. She explains that as a Shinigami it is her job to help spirits pass on to the afterlife, to a world called the Soul Society.
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That same night promises to be an interesting one as the Kurosaki household comes under attack. A Hollow, which is an evil and sinister version of spirits, seeks out Ichigo and wants to devour him.
The Shinigami woman tries to fight against the Hollow in order to defend Ichigo but suffers a mortal wound.
In a desperate last-ditch effort to save them both, the female Shinigami tells Ichigo to run her sword through him, in order to become a Shinigami himself. She then finally tells him her name ... Rukia Kuchiki.
Rukia runs Ichigo through with her Zanpakuto, the weapons of Shinigami and transfers some of her powers to him.
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The transfer was a success. Ichigo, now a Shinigami himself and wielding a colossal blade manages to defeat the Hollow.
However ... the transfer of powers worked too well. Rukia who initially only wanted to transfer 'some' of her powers to Ichigo, has been stripped of all her power instead.
This leads to her being stranded in the World of the Living for the time being. So until her powers can return to her, Ichigo takes on the role of a Substitute Shinigami. Filling in for Rukia and defending the residents of Karakura town from Hollows including his close friends Orihime Inoue and Yasutora 'Chad' Sado.
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Ichigo undertakes a variety of missions. Ranging from capturing a renegade called Kon a mod soul, to helping Don Kunochi, a famous TV personality best a Hollow in the Hospital.
He even encounters the Hollow that was responsible for his mother's death, Grand Fisher. After getting seriously wounded Ichigo manages to deal a critical blow to the Hollow and forces him to flee.
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After Ichigo settles into his role as a Substitute Shinigami, his beliefs are challenged by a boy in his class, Uryuu Ishida. A mystical archer who calls himself a Quincy with a vendetta against Shinigami.
This hatred comes from the fact that his clan the Quincy were wiped out 200 years ago by the Shinigami.
The two try to find out who is the stronger between them and Uryuu uses what he calls Hollow bait to bait Hollows and then kill them all.
Things quickly get out of hand though.
During this fight, Orihime and Chad develop powers of their own. Uryuu and Ichigo manage to put their differences aside to fight a Menos Grande. A towering giant Hollow.
Ichigo shows his latent potential and strength when he manages to force the Hollow to retreat.
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Everything seems to go well for Ichigo and his friends until one night.
That night, two shadowy figures arrive in Karrakura Town to arrest Rukia. The two figures are high-ranking Shinigami from the Soul Society. Vice-Captain Renji Abarai and Captain Byakuya Kuchiki of the 6th Division, who happens to be Rukia's older brother.
Rukia is to be arrested for the 'grave' crime of giving a human Shinigami powers causing the Soul Society to issue a warrant for her arrest.
Ichigo, true to his name, tries to save Rukia and even momentarily manages to defeat Renji. The victory is short-lived though as he suffers a devastating defeat at the hands of Rukia.
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Ichigo is rescued on the brink of death, by the mysterious Kisuke Urahara, the owner of the local Urahara candy store. A shady man with a hidden agenda and historical ties to the soul society.
"Now now, you shouldn't be up, Mr. Kurosaki. Your wounds haven't healed yet. You'll die if you move around too much.", Urahara tells Ichigo after the latter wakes up in Urahara's shop the next day.
"I see. So this is your house."
"Correct."
"Did you save me?"
"Well, that tone is unexpected. It sounds as though you didn't want me to rescue you.", Urahara mentioned.
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Ichigo is depressed and angry that he can do nothing to save Rukia.
"There is no way .."
"Do you really believe that? The way to get to the Soul Society ...", Urahara starts but doesn't finish his sentence.
"Is there a way to get there? How? How do I get there?! Tell me!"
"Of course, I'll tell you. But there's one condition.", Urahara tells him.
"Condition?"
"Yes. For the next ten days, study with me on how to fight."
This marks the moment when Urahara takes Ichigo under his wing. Promising him to not only unlock his own Shinigami powers but make him strong enough, in ten days, to take on the Soul Society and rescue Rukia.
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In Urahara's training area, Ichigo's soul form is freed from his body, and he finds it difficult to move. Urahara reveals Byakuya destroyed the source of his power, leaving him without any Shinigami powers, and he must restore these in order to fight the Shinigami.
Ichigo has to go through 3 trials and finds himself within his inner world. A spiritual place within every Shinigamis soul where he talks with a strange man in a black coat.
Eventually, Ichigo even becomes a Hollow through the brutal tests of Urahara Kisuke before understanding his Shingami powers and transforming.
After that Urahara starts the third lesson, which is simply to knock the hat off of Urahara's head. As Ichigo proposes a five-minute time limit, Urahara draws a blade from within his cane, revealing his own Zanpakuto, Benihime.
As Ichigo, thinking he is going to die, runs away, Urahara continues to attack him. Ichigo sees the man from his inner world again, who, asking why Ichigo ran when he has not yet called him, reveals his name is Zangetsu. Stopping in his tracks, Ichigo, turning towards Urahara, calls out Zangetsu, activating his Shikai.
After continuing their training for a few days, Ichigo's friends Orihime and Chad come together at Urahara's shop.
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"W-wow! All this space beneath the shop! This is so neat ... it's like a secret base!", Orihime says.
"Really?", Ichigo asks.
"All right, your attention please! Here we go!", Urahara says and then snaps his fingers.
"This is the gate that leads to Soul Society. It's known as the Senkaimon, which is written, "Tunnel World Gate." Now listen very carefully. Before that ..."
Urahara then removes Ichigo's Shinigami form from his physical body.
"Hey at least warn me before you do that.", Ichigo tells him.
"Let's continue. This gate has a layer of Reishihenkanki, a Spirit-particle Conversion machine on top of a normal Senkaimon.", Urahara continues.
"Spirit particle ... machine?", Ichigo asks.
"Yes. As you already know, the Soul Society is a world of spirits. It is impossible to enter that world unless you have the form of a spirit. However, only Ichigo, as a Shinigami, can cross through.
So we will use the Henkanki to convert you into spirits.", Urahara explains.
"In other words ... We'll be able to pass without extracting our spirits, by going through this gate.", Uryuu says.
"Correct. You will be able to enter the Soul Society like that."
"Okay, got it! Let's get-", Ichigo has heard enough and want's to go, but Urahara stops him.
"However ... The time limit that we have to open the gate and connect it to the Soul Society is ... four minutes.", Urahara reveals.
"I-Is that enough time?!", Ichigo asks him.
"Normally it would be impossible. It's a reckless idea to start with. I'll do my very best and hold it for four minutes. If you can't cross over in that time ... you will be trapped forever between the Soul Society and this world.", Urahara reveals.
"W-what should we do?", Orihime asks.
"Just go forward.", the male voice of the black cat is heard.
"I told you that the heart and the soul are connected. The important thing is what you feel in your heart and the will to move forward. I will be your guide.
Go forward ... Only those who can do that can follow me.", Mr. Yoruichi finishes.
"Are you babbling in your sleep or what? That's why we're here!", Ichigo tells the cat.
"You understand, kid, that if you fail, you cannot return."
"So I just have to win, right?"
"Exactly."
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Urahara and Tessai start the Senkaimon which begins to shine brightly.
"Are you ready? Run the instant it opens.", Urahara tells them.
Entering the gate, Ichigo, Uryuu, Orihime, Chad, and Yoruichi appear in the Dangai. The group are chased by the Kōtotsu which is a cleaner of the Dangai, and Orihime uses her shield to protect them from it, propelling them through the exit and into Soul Society.
The group exploded into the Soul Society and landed in the Rukongai district.
"I'm so glad everyone is unhurt.", Orihime says and is then hit in the eye by Yoruichi.
"What is there to be glad about? Weer you not listning to me?! We're lucky the Restritive Current made contact with just the shield area. If it had been the Shunshunrikka themselves, you'd be dead now!", Yoruichi explains and reprimands Orihime.