The 9-volume series (properly pronounced as "Gahn-mu" (Gun Dream)) follows the life of Gally. She is a small female cyborg discovered and named by Ido, a cyborg engineer who had found her head and part of her torso in a junk heap. (In the U.S. version, her name is Alita (see side note below)).
Their city, Scrap-Metal City, is a crime-filled, dangerous place, but above it, connected by massive tether-conduits, floats the mysterious city of Zalem, rumored to be a high-tech paradise. Periodically, Zalem dumps garbage to the ground below, and it was in one of those mountains of trash that Gally had been found. Ido himself is an ex-inhabitant of Zalem, but won't speak of it.
Gally, who has amnesia and can't recall who she was, lives happily with Ido for a while. But gradually she becomes involved in the dangerous business of bounty-hunting, discovering at the same time that she has an affinity for fighting and killing. She finally falls in love with a boy named Yugo --- but to her horror, he winds up on the bounty list. In the end, she saves Yugo, but he follows his dream of climbing up to Zalem and dies in the attempt.
Gally and Ido have a falling out. She takes up tournament combat, becoming quite a popular fighter. But she seems to draw disaster like a magnet, and eventually even her friends turn away from her as her enemies try to hunt her down. Finally, screwed over by the system, she nearly dies, but is rescued by agents of Zalem. She sells herself to the technicians of Zalem, to be their agent/warrior on the Earth as a "TUNED" agent; she is linked into their computers, and technicians oversee her actions. Drunken with battle power, addicted to the white blankness of the heat of combat, it isn't until she finds a lover (Fogia) that she feels some sort of meaning to her life. Respite is brief, and she quickly plunges back into the messier side of life, seeking to bridge the gap between the mysterious paradise of Zalem and the mean, dirty streets of the Earth. Her nickname is "Angel of Death," or "Evil Angel," but she never loses her humanity or her basic compassion for innocent people. She discovers Ido is gone from her forever, and cries; she discovers that Zalem has played a cruel trump card and has created replica androids of her, and tries to destroy them. She is still caught between Zalem and the people of Scrap-Metal, and sees coldness on one side, and over-bright rage on the other.
She even remembers her previous life as a cold-hearted terrorist named Yoko, and rejects it. Finally, the series culminates with Gally arriving on Zalem itself. It is a form of paradise, a last remnant of peace and ultra-high tech. But most of the people are weak-willed sheep, happy to live and die that way. By now, Gally has already found out some of Zalem's secrets; now, enraged by the passivity of the people, she finds out its ultimate purpose (it is the lower half of an orbital space port called Jeru-Salem) and its ultimate lie. Both aided and hindered by her arch-nemesis, the mad scientist/nanotech-engineer Nova, she has, she realizes, been given the power to judge Zalem and destroy it utterly; she, the battle-hardened killing machine, is more than a match for anything on Zalem. Zalem's main computer, realizing Gally may well bring its reign to an end, would rather commit suicide than allow this to happen. It is up to Gally, with Nova's help, to save both cities --- Zalem and the one below it. And so Gally brings about a final end to the floating city in an astounding transformation. The people of the Scrap-Metal City and Zalem are reunited again.
....
It's unfortunate, but the last book was somewhat rushed and a little bizarre, probably due to the author's severe illness (he was publishing at half his normal rate, and in fact missed several issues of Business Jump). But the wonderful artwork remained the same throughout: fine tech-work, flowing combats, fascinating characters, and always Gally --- small, fast, light, grinning from behind her blazing gun. Gunnm is a "Gun Dream," a dark, harsh, but not inhuman image of the future.
Side note: Amusingly, in one hallucinogenic cyber-dream sequence (induced by the mad Dr. Nova), Gally relives a twisted version of her early life with Ido --- in which she has been named "Alita" by Nova. Since this happened well after the initial U.S. release of Battle Angel Alita, one must assume that the author was satirizing the name.