I don't read a lot of manga, and when I do it's usually the girly kind, but since a co-worker insisted that I give it a chance here we are. It's set in a dystopian future (is there any other kind?) where a apparently wonderful city floats over the Earth. The refuse and the unworthy people live on Earth, and modify their bodies with cybernetics in order to survive.
Daisuke, a tinkerer of sorts, finds Alita among the garbage and in a paternalistic twist tries to fix her and protect her from the filth. He's not only a scientist but a hunter as well. The first story arc is very interesting, a mix between Jack the Ripper and Frankenstein. The payoff does not deliver though because even though this is meant to be a very dark story, it's surprisingly upbeat. Alita is ever positive and ever chirppy. Alita always triumphs and it's not because she has an awesome killer body (literally!) but because of her spirit.
The art is pretty standar manga fare but I'm sure it turned heads when it was first published. The color pages you sometimes find on the beginnings of collected volumes here are drenched in fine crosshatching and ink washes and I kinda wish the whole comic was like that.
I would be interested in reading more about Alita just to see how she matures as a person and how that affects her realtionship with Daisuke.