This one shot is composed of four separate side stories for Battle Angel Alita, known in Japan as Gunnm. 
Before being compiled as one single volume in 2007, the short stories were first published in Ultra Jump in 1997 and 2006. Three of them ("Furusato", "Seiyakyoku" and "Sonic Finger") had also been included in the Japanese Gunnm: Complete Edition. In 2018, all four stories were published in English in the Battle Angel Alita Deluxe Edition box set. 
Several characters who appear in the side stories do not appear in the regular manga. The side stories also provide more background on the Factory and motorball. 
(Source: Wikipedia)

In a dump in the lawless settlement of Scrapyard, far beneath the mysterious space city of Zalem, disgraced cyber-doctor Daisuke Ido makes a strange find: the detached head of a cyborg woman who has lost all her memories. He names her Gally and equips her with a powerful new body, the Berserker. While Gally remembers no details of her former life, a moment of desperation reawakens in her nerves the legendary school of martial arts known as Panzer Kunst. In a place where there is no justice but what people make for themselves, Gally decides to become a hunter-killer, tracking down and taking out those who prey on the weak. But can she hold onto her humanity as she begins to revel in her own bloodlust?
 
(Source: Kodansha USA, edited)

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