For a few seconds, Moon-Watcher stood uncertainly above his new victim, trying to grasp the strange and wonderful fact that the dead leopard could kill again. Now he was master of the world, and he was not quite sure what to do next. But he would think of something. (5.10-11)
Moon-Watcher has taken the first step up the evolutionary ladder. That cuts him off from the other man-apes to some extent; he's isolated by power. Evolving is a lonely business.
Part 3, Chapter 18
Though they were perfectly well aware that 7794 was only a lifeless, airless chunk of rock, this knowledge scarcely affected their feelings. It was the only solid matter they would meet this side of Jupiter—still two hundred million miles away. (18.9)
The astronauts get all sentimental about a hunk of rock out in space. It's another chance for Clarke to point out that the middle of space is a long way from home.
Part 4, Chapter 27
… he would continue the mission, unhindered and alone. (27.11)
Hal the computer figures he can kill all the astronauts and then go on his way to complete the mission. Part of the eeriness is that Hal isn't really a person himself, so Hal alone is more lonely than lonely.
Part 4, Chapter 28
There was not another human being within half a billion miles. And yet, in one very real sense, he was not alone. Before he could be safe, he must be lonelier still. (28.25)
Hal figures isolation will be safe…and David Bowman comes to the same conclusion. One thing about being isolated, you know no one will kill you. People (or, in this case, computers) are dangerous.
Part 5, Chapter 33
During the last three months, David Bowman had adapted himself so completely to his solitary way of life that he found it hard to remember any other existence. He had passed beyond despair and beyond hope, and had settled down to a largely automatic routine…(33.1)
In isolation, Bowman has become computer-like. It's like he's merged with Hal. Or as if the novel tends to view humans like computers, and enjoys watching them run through routines.
Part 5, Chapter 38
It if had been alive, it would have felt excitement, but such an emotion was wholly beyond its powers…It had waited three million years; it was prepared to wait for eternity. (38.7)
The Star Gate feels nothing—so why imagine it as feeling something? The suggestion is that it's a kind of computer, like Hal, similarly singularly focused on its mission. The purposeful isolation is meant to be eerie and impressive.
Part 6, Chapter 42
Bowman wondered if this was indeed his own galaxy, seen from a point much closer to its brilliant, crowded center. He hoped that it was; then he would not be so far from home. But this, he realized at once, was a childish thought. He was so inconceivably remote from the Solar System that it made little difference whether he was in his own galaxy or the most distant one that any telescope had ever glimpsed. (42.3-4)
Bowman is more isolated here than any human has ever been. Yet he chides himself for wishing he was a little closer to home. It's like the novel doesn't want you to think for a second that Bowman might be illogical, or might except illogical thoughts. No matter how isolated, he's just sane, stable, boring old Bowman. We've got to give him props for consistency.
Part 6, Chapter 43
He was moving through a new order of creation, of which few men had ever dreamed. Beyond the realm of sea and land and air and space lay the realms of fire, which he alone had been privileged to glimpse. It was too much to expect that he would also understand. (43.16)
Bowman is going where no one has gone before. He is, literally, far out.
Part 6, Chapter 45
David Bowman moved into a realm of consciousness that no man had experienced before. (45.4)
The strait-laced Bowman becomes the ultimate hippie, expanding his consciousness the natural way, via alien intervention. (The visuals for 2001 in the film are extremely trippy; Bowman may be a boring square, but the aliens definitely listen to the Beatles.)
Part 6, Chapter 46
Then he remembered that he would never be alone, and his panic slowly ebbed. (46.13)
It's not exactly clear what this means, though the suggestion seems to be that Bowman shares some sort of super-consciousness with the aliens. So humans and aliens really do fuse; the novel ends with humankind no longer being alone, not even in its skull. This is supposed to be a good thing, though you could also see it as maybe a little intrusive.