The sequel to Neuromancer, but quite a ways down the road. There are a few secondary characters from Neuromancer who show up in this story, but it does stand alone very nicely. I think. It has been a while since I read Neuromancer, and I may have missed making a few connections here and there.
There are 3 main characters, 2 of whom do finally meet near the very end of the book, and the 3rd who is there to give the reader a much different perspective on what is actually happening in the world.
Turner is a mercenary who specializes in extracting top level scientists from the companies who essentially own them and arranging for them to defect to a new company. The companies would often prefer to kill the scientist in question rather than lose them to a competitor, so this can get pretty messy. Turner has essentially just been rebuilt from the ground up following an explosion after his last job went badly. Now he's back on the job, extracting yet another research scientist.
Marly is a disgraced art gallery owner who has just been hired by the richest man on the planet in order to track down the source of some very unusual pieces of artwork. In the process she gets to discover just exactly how different the ultra-rich are from regular folks - her employer lives entirely in cyber-space while what remains of his body lies in a giant tank somewhere in a bunker in Stockholm.
Finally there's Bobby Newmark, aka Count Zero, who really wants to be a "console jockey". This is where it becomes really obvious that this book was written in 1986, and you can see how Gibson's idea of Cyberspace, while really cool, is very very different from the internet as we're familiar with it. A console jockey appears to use a keyboard for input, and manual dexterity is definitely important. They're linked in to Cyberspace via electrodes attached to the forehead, and the experience appears to be very much like riding a motorbike through a shifting 3D landscape. The problem with Bobby is that he is very inexperienced, and doesn't actually seem all that good at what he wants to do. He's just a script kiddie. But he has accidentally wandered into the middle of something much bigger than he is, and while he is just a teenage boy, he really does his best.
Having finished this, what I really want to do is to read Mona Lisa Overdrive, then sit down and read all 3 of these books back to back. There is some really cool stuff going on conceptually, but I find with Gibson that I really have to pay attention to the pictures he is drawing in my head, otherwise things stop making sense very quickly. This isn't the sort of story you can just skim over, he expects a reasonable amount of effort from his readers...which is awesome...except that it really does take some work.