it's really hard to summarize a whole series, here's the intro:
a girl (faye valentine) was in a coma of some sort, she just now realizes that she's missed 30 years or something of her life, and some dude put her in rehabilitation to get her memory back, she falls in love with him and it's all good, then he gets killed when someone tries to hunt her down, and she ends up inheriting everything he ever owned, even his debts, so she has to work as a card dealer to pay it all off and then her boss gives her this job to steal something and now she's got a bounty on her head, that's when a bounty hunter tries to capture her to get the money and that's where the story gets interesting...keep in mind, my summary is not in order, you don't know any of this until later in the story, but trust me, it's a good series...don't watch the ones on adult swim tho, subtitles are better than dubbed.