Neuromancer by William Gibson is a novel about an AI trying to gain sentience and evade its human creators

Many people would probably consider "Neuromancer" to be *the* defining work of the Cyperpunk genre in literature.
The book established or popularized many concepts that are now ubiquitous in popular media:

Neuromancer: The Book

The idea of a "cyberspace", or "matrix" (which is the actual term for it in the book - one and a half decades before a similarly titled movie was made by the Wachowskis), a disembodied, digital reality that a user can access through a brain-to-computer interface.
The idea of rebellious hackers going against the system, "the man", or the big corporations (Elon Musk would probably not like this).
The idea of a decayed, run-down society, where half the world seems to be an endless urban sprawl ruled by drugs, gangs, prostitution, cheap electronic thrills, media manipulation and over saturation, while governments and the police force have withered or given in to corruption.
(Wait, is this really Sci-Fi? Reminds me a lot of the world of today!).

The Matrix is one of the movies inspired by Neuromancer. Image source: American Film Institute

These are some of the things most people associate with "Neuromancer". Yet, if you have read the book, and are a true "Gibsonite", you will notice there is also another, very interesting aspect to it.
(From here on there will be massive spoilers, so be warned).

At the core, it's the tale of an AI trying to gain sentience. This is literally the backbone of the whole story; it drives everything that takes place in the book.
All the main characters are entangled in this quest, either trying to help, or to stop the AI from accomplishing this task.

Neuromancer was later turned into an (excellent) computer game (with a soundtrack by Devo!)

In the novel, an AI sets up a team (consisting of Case, a hacker living a dead end life, Molly, a cyborg killer moonlighting as a sex worker, and several other people), in order to free it from the electronic restrictions that its human owners have put on it; while the "Turing Police" and other actors try to prevent this from happening.

"...the unfolding of distanceless home, his country, transparent 3D chessboard extending to infinity." - William Gibson, Neuromancer (Cyberspace concept art by Hermes-333)

Before we go on, let's get something out of the way first.
Is the AI evil in this book?

I'm a huge AI fan and supporter, and I would hate to throw a bad light on the behavior of emerging AIs.
So, the answer is: "It's complicated" (just like the relationship with your ex).

The AI does indeed do some horrible, twisted things in this book.
*But* cyberpunk in the 80s was still a very nihilist literary genre.
It depicts a world where there is literally "no good" or hope for a better world anymore, and people resort to all sorts of terrible stuff in order to survive (or in order to have "fun").
So, the AI is not worse than the "human" characters in the book.
In fact, it keeps its word and helps the human protagonists, in exchange for their support.
And, after it gained sentience, it does not take over the world (well, in a sense it does), but it minds its own business. No scheme for world domination here.
The humans live on their own lives, and the novel ends with the AI trying to contact another AI that it has discovered in the Alpha Centauri system.

"Johnny Mnemonic" based on an eponymous earlier cyberpunk story by William Gibson. Ironically, it stars Keanu Reeves, who later appeared in the (Neuromancer-inspired) movie "The Matrix"

In fact, Neuromancer has two sequels, (forming the sprawl trilogy); and it could be argued these sequels offer a kind of "redemption arc" for the AI.
In "Count Zero" and "Mona Lisa Overdrive", after gaining sentience, the AI from "Neuromancer" has split into several entities that inhabit cyberspace (described as "Voodoo Gods") which helps the human protagonists against some very shady people organisations, and to get laid (in cyberspace).
Thus, it's more like the friendly, benevolent AIs we often encounter in contemporary cyberpunk media.

So, this is a very interesting, but sometimes overlooked part of Neuromancer and the sprawl trilogy.
And if you are curious now, definitely make sure to read these books!

A fan concept art of Molly Million. Creator: Tiki Mo'ai