The book opens way, way, way back, when men were ape-things and women were too.
The setting is Africa, the Equator, prehistory, and the man-apes are having a bad time of it because there's a nasty drought.
No water means no food; no food means lots of starving man-apes.
Moon-Watcher (your man-ape protagonist for this first bit of the novel) finds that his father has died.
Moon-Watcher is smarter than your average ape, the book says. Still, he's got to drag his dad (the Old One) out to bury him.
Moon-Watcher checks to see if the enemy tribe/group, the Others, is around. They're not.
He forgets them. He can't think of more than one thing at a time.
2001 presents its man-apes as being almost dumber than house cats. Remember, Shmoopers, this is science-fiction, not science. Don't write "apes are dumber than house cats" on your science exam, or you will do poorly.
He leaves his dad's body under a bush, where hyenas and scavengers will eat it.
Not much room for sentimentality there among the man-apes.
He goes to pick some berries with other members of his group. It's a pretty good day for picking berries; they get enough food so that they're not actually starving.
They run into the Others at the stream. They yell and beat their chests at each other, then all go about their business.
They get back to the cave and Moon-Watcher gives an injured female some berries.
They go to bed in their cave on the mountainside.
They are woken up by some predator killing and eating someone further down the mountain.
It sucks to be a man-ape.
The man-apes are the first creatures to look at the moon, the novel says, and Moon-Watcher used to try to grab it when he was little.
And while he's dozing something very bright passes across the sky.
That's foreshadowing, Shmoopers. (Hint: it's a spaceship.)