Battle Angel Alita, Complete Box Set, Deluxe Volumes 1-5 plus Short Stories (by Yukito Kishiro)

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 Alita and equips her with a powerful new body, the Berserker. While Alita 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.