The future was, very literally, in their own hands. (4.6)
The man-apes hold the future in their hands because their hands, and the tools in those hands, will be their future. Technology takes you to the future, to the moon, and out into space, where you are turned into an alien space-baby.
Part 1, Chapter 6
They had learned to speak, and so had won their first great victory over Time. Now the knowledge of one generation could be handed on to the next, so that each age could profit from those that had gone before. (6.7)
History is seen as a victory over time—but you could just as easily see it as a kind of victory of time. After all, if you're a happy man-ape, without speech, living day to day, you don't know that time is passing. It's only with history and knowledge passed on that time really comes into being as a big weighty thing sitting on your forehead.
Part 2, Chapter 12
Three million years! The infinitely crowded panorama of written history, with its empires and its kings, its triumphs and its tragedies, covered barely one thousandth of this appalling span of time. Not only Man himself, but most of the animals now alive on Earth, did not even exist when this black enigma was so carefully buried here….(12.11)
The slab is three million years old, which is really old. It's older than the human race (or about the same age, if you count the man-apes). Time here is presented as awesome or amazing in itself. Time—it will surprise you.
Part 3, Chapter 15
Though he had come back safely from the furthest borders of sleep, and the nearest borders of death, he had been gone only a week. (15.37)
Hibernation fiddles with time…and as such it's kind of like reading the book, don't you think? You can go to the furthest borders of sleep and the nearest borders of death and 3 million years into the past in only about a week if you read 2001. Hibernation is a kind of reading, only maybe colder.
Part 3, Chapter 20
The ancients had, indeed, done better than they knew when they named this world after the lord of all the gods. If there was life down there, how long would it take even to locate it? (20.14)
This is about the planet Jupiter. As always in 2001, space is quickly linked to time; "the ancients" named Jupiter, reminding you that the planet has been there the whole time, just hanging out and being big.
Part 4, Chapter 21
How strange to think, Poole told himself, that all this had happened more than an hour ago; by now his family would have dispersed again and its members would be miles from home. (21.3)
The distance from earth (through space) is emphasized by disjointed communication. When you go far enough away, time gets stretched out too.
Part 5, Chapter 32
These arguments, theoretical though they were, concerned a matter of the utmost practical importance; they involved the concept of "reaction time." (32.9)
How long is it going to take the aliens to get to earth? The answer, as it turns out, is "no time at all." The aliens have mastered space, which means they have mastered time, just like their mastery of the past and all those man-apes reflects their mastery of the future. The aliens are everywhere and everywhen. They're tough to get away from.
Part 6, Chapter 41
The seconds themselves were passing with incredible slowness, as if time itself were coming to a stop. At last, the tenth-of-a-second counter froze between 5 and 6. (41.7)
Einstein's theory of relativity linked travel through space and time—basically, as you approach light speed, time appears to slow down from your frame of reference. Something like that is happening to Bowman, whose watch slows down as he goes through the faster-than-light transportation of the Star Gate (This would be convenient if you're ever late to an appointment, obviously.)
Part 6, Chapter 45
He was retrogressing down the corridors of time, being drained of knowledge and experience as he swept back towards his childhood. (45.8)
This is the second time retrogression occurs in the novel. The first is when Bowman unplugs Hal, making him regress to when he was just a baby calculator. Again, this reflects the way the novel treats time and space—you go into the stars to find the past, and so Bowman on the other side of the galaxy regresses to a (super space) baby.