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Specifically, it needs expansion on 57th expedition.
The original squad was considered the most elite squadron, having a total kill record exceeding 200, and were capable of killing almost any Titan in their path. Due to their strong bond, they were able to synchronize with each other to coordinate their attacks without direct or verbal communication. During the 57th Expedition, their mission was to protect Eren Yeager from Titans, and their secret objective became to lure the Female Titan into a trap. The mission failed, and all the original members of the Special Operations Squad, except for Eren and Levi, were killed.
After the events of the supposed breach of Wall Rose and the massacre during Eren's rescue, Levi forms this squad anew with its members being the remaining soldiers of the 104th Training Corps' Top 10 and Armin Arlert in order to watch over Eren and Historia Reiss.
The Special Operations Squad is hand-picked by Levi himself. They watch over Eren Yeager during his Titan transformation experiments in the days leading up to the 57th Expedition. On the expedition itself their mission is to protect him and they do not engage in the rest of the operation. After they see the signal flare to return, they mistakenly believe the mission is successful and plan to leave. During their departure, they think they see Levi returning to them, but it turns out to be an unexpected assailant. Gunther Schultz is killed by a disguised Annie Leonhart who then transforms and kills Petra Ral, Oluo Bozado, and Eld Jinn.
After Eren is rescued from Reiner Braun and Bertolt Hoover, the Armored and Colossus Titans, Levi takes it upon himself to form a new Special Operations Squad. The new team consists of the remaining members of the 104th Training Corps' top ten graduates and Armin Arlert. They serve to protect Eren and Historia Reiss after the latter is discovered to have a familial connection to the Walls.
Their first assignment as a squad involves hiding out in a remote cabin so Eren and Historia are away from prying eyes and Eren can practice with his Titan without being seen. Finding out the capabilities of his Titan is critical for the recovery of Wall Maria. Most of the squad secures the perimeter of the test area to make sure there are no witnesses. However, Eren's attempts to harden his Titan are unsuccessful and the squad is soon called back to Trost District by Erwin Smith.
Knowing that Eren and Historia are targets, the squad proceeds into Trost without them. Jean Kirstein is disguised as Eren and Armin Arlert as Historia. The two decoys are kidnapped in their place, allowing the squad to track the kidnappers without risking the loss of the people they are protecting.
The remaining members of the squad tail the kidnappers into a hideout, and hiding until their leader arrives. Levi's ankle is healed, so he is able to join his squad-members in incapacitating the kidnappers in a brawl. The squad tie up the kidnappers once the fight has concluded and bring Dimo Reeves on top of the Wall for questioning and negotiations. An agreement is made, binding the Reeves Company and the Survey Corps together.
The Special Operation Squad return to standby, and in the morning, Nifa delivers a message from Erwin to the members and Reeves, revealing the plan to have Historia take the throne. This plan is met with shock, and the idea is initially rejected by Historia, but Levi pressures her into agreeing to her new position.
Eren and Historia agree to be kidnapped by Dimo Reeves, in order to lead the rest of the squad to Rod Reiss, the true ruler of the Walls. This plan goes horribly wrong, however, when the Anti-Personnel Control Squad assassinate Dimo Reeves and his men for conspiring, leaving the Survey Corps to take the blame. All Survey Corps members are called in for arrest, though the Special Operations Squad ignores those demands.
The Special Operation Squad pursues Eren and Historia over the next two days. In Stohess District, the squad finds the two being placed into a hearse. However, the stakeout is ambushed by Kenny Ackerman and the Anti-Personnel Control Squad. Three members from Hange Zoë's squad are killed. Levi barely manages to escape and return to his squad, having to kill some of the MPs along the way.
He gives the order to stop pursuit of the hearse, and to escape the district. During the escape, Jean ends up at an MP soldier's gunpoint, though Armin manages to save Jean by shooting the woman himself. This action allows the squad to safely escape the District.
The squad plan to infiltrate the brigade, to gain directions to the Military Police's Interior Brigade compound, in hopes of finding Eren and Historia. They capture Hitch Dreyse and Marlowe Freudenberg, though they prove to be cooperative, and offer to show them the way to the compound themselves.
At the Interior Brigade compound, the squad debilitates all of the Military Police present. They are more ruthless than they had been before, due to Jean's brush with death, though they attain no new information. Later, Hange arrives and brings the news that the SC have had their charges lifted. She is also able to deduce the location of Eren and Historia; a village chapel that Rod Reiss had rebuilt after a fire.
At the chapel, the squad discover an underground cave where Eren is being held and Historia is preparing for a family ritual. They prepare for battle with the Anti-Personnel Control Squad. When the fight begins, the Special Operation Squad quickly exploits the weaknesses of the anti-personnel vertical maneuvering equipment. Traute Carven manages to injure Hange before ordering a retreat. Levi leaves Armin with Hange and pursues with the rest of his squad.
Rod Reiss transforms into a Titan as the squad ventures deeper into the cavern. They find Eren chained and Historia trying to free him. As the roof collapses around them due to the size of the Titan, the squad frees Eren, but finds no way to escape. After being told to make a choice by Levi, Eren decides to transform into a Titan, and seals up the cavern by using his newly acquired hardening power.
The Special Operations Squad members are able to secure an exit out of the cavern and meet up with the rest of the Survey Corps in order to solve the problem of Rod Reiss' Titan, which is ignoring them despite the fact they are the nearest humans around. Eren attempts to command it as he had done with other mindless Titans, but his power does not work.
They race to Orvud District, where the Special Operations Squad helps Hange and Moblit Berner set up a web of explosive charges for use against the gigantic Titan. After the Titan comes within range, Eren shoves the net full of gunpowder into its open mouth, where the heat of the Titan is enough to cause the explosives to spontaneously combust. The Titan's head explodes into numerous pieces and the squad flies out to cut the piece containing the nape. Historia lands the final blow herself.
The current members dwindle from seven to six after Historia Reiss becomes queen, as she remains behind when the Survey Corps executes their mission.
During the mission in Shiganshina, Squad Levi is fragmented even more. After Armin reports to Erwin about finding three teacups, he is placed in charge of a team to search around the inner gate for enemies. At this time, the rest of the Squad is ordered to wait on standby atop the Wall. After Reiner is located and injured by Levi, he transforms into the Armored Titan.
Erwin orders Squad Levi and Squad Hange to take down the Armored Titan, however, Levi is instructed to help guard the horses. Armin rejoins Squad Levi as its interim leader. Commander Erwin gives orders to use Eren as bait in order to lure Reiner away from the horses. This plan is carried out successfully, leading to the two Intelligent Titans engaging one another.
At a stalemate during the fight, Squads Hange and Levi use the opportunity to surround Reiner and use the Thunder Spears to blind, shatter, and then decommission the Armored Titan. The squad grieve over Reiner for a while, lamenting the lack of opportunity for any negotiations. When Bertolt is thrown over the Wall, the two squads pull back from the area, though when he does not blow the area away, Armin seizes the opportunity to negotiate with him. When this negotiation fails, Bertolt flies up and transforms, the energy creates a devastating blast that rips through Shiganshina and kills the members of Squad Hange.
The squad take cover before regrouping. They then watch the Colossus Titan spread flaming wreckage across Shiganshina. Armin gives an unsure order to fight a war of attrition against the Colossus Titan, however Jean points out the flaws in this plan. This makes Armin ask him to take over command. The squad then temporarily moves to the river.
Later, Eren yells to draw Bertolt's attention, however, he is ignored in favor of going towards the Wall. Eren attempts to push back the Colossus Titan, though this attempt ends up being counter-productive, as Bertolt kicks Eren atop the Wall, incapacitating him. The rest of the squad attempt to fight Bertolt using a diversion tactic, however he sees straight through this plan, repelling the Squad and Mikasa's Thunder Spears using steam. After this, the Armored Titan stands up, ready to rejoin the fight.
Armin notices the Colossus Titan is skinnier, and forms a plan for him and Eren to take it down. He requests the rest of the squad draw Reiner away, before flying off to wake Eren.
As Eren and Armin prepare for the rematch, the rest of the squad fly to engage Reiner. Mikasa blows his leg, immobilizing him in place. After creating a plan, they set it into action. Jean acts as the bait, and Sasha and Connie fly to blow the hinges of Reiner's jaw. However, Reiner hits wreckage towards the attackers, hitting Sasha and Jean, and making Sasha's Thunder Spear miss its mark. Hange returns and hits Reiner's jaw instead, giving Mikasa the opportunity to blow Reiner out of his Titan's nape.
Armin and Eren successfully take down Bertolt, though Armin is burnt to the verge of death in the process. Levi also returns from over his side of the Wall, having chased the Beast Titan all the way. The rest of the squad rest as Reiner is interrogated by Hange. They debate stealing the Power of the Titans from Reiner, giving it to the moderately injured Sasha. Mikasa is sent off to scout the situation and locate Levi, whilst the others wait. Later, Reiner is recovered by Zeke, though Jean manages to save Hange from the Cart Titan.
The Special Operations Squad fully reunites amidst a violent confrontation between Eren and Mikasa against Levi, over the Titan injection. Levi plans to inject Erwin and have him eat Bertolt, ordering to clear the area to accomplish this. However, Levi changes his mind, instead injecting Armin. Eren, Mikasa, Jean, and Connie help Armin out of his Titan. After this, the squad separates, searching the battlefield for survivors but finding none. A few Survey Corps members clear the basement before the nine survivors return to Trost.
Several months pass and eventually all the remaining Titans within Wall Maria are killed or destroyed and people return to repopulate Shiganshina District. The Special Operations Squad then sets out for the first expedition beyond Wall Maria in six years. While many of them are surprised by the lack of Titans in the area outside Wall Maria, Hange theorizes that it is due to the majority of the Titans invading Wall Maria five years prior. They eventually reach a Marley military structure where Eldians were taken to and turned into Titans: beyond that, they finally reach the coast and bear witness to the ocean for the first time, the only thing now seperating them and the nation of Marley.