From Kodansha US,:
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. In a place where there is no justice but what people make for themselves, Alita 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?

Official:.
Kodansha, Cómic Days, Comico, Lezhin, Pixiv Comic

Official Translation:

• English: Kodansha US, Azuki, KManga, INKR, Manga Planet
• French, Germany, Chinese, Spanish, Serbian, Italian, Polish, Portugese (Print, Digital),

Note: The second half of Chapter 51 (Epitaph) and the rest of Vol 9 were replaced in continuity by Gunnm Last Order.