Mankind's been expanding at sub-light speeds for many generations, sending out Bussard ramjet propelled probes to investigate possible systems, and colonising ships to any suuitable planets (and at least one asteroid belt which, since a largish proportion of astronauts are belters rather than flatlanders should suit them quite well)
During this expansion they ran into the Kzinzi, an agressive, lion like culture that had got into space by enslaving the more advanced race that discovered them ( they'd never have been able to co-operate enough on the research to make it on their own.)
During this war the outsiders (that's the cold, photoelectric ones) sold the secret of the hyperdrive to humanity, not to the kzinzi, Victory for humans, pick up the pieces, take over a number of races enslaved by the kzinzi. A generation – a long generation, with boosterspice – of consolidation, and they're starting to explore again. They know ( the leaders know) that the core of the galaxy is exploding, and in a hundred thousand years or so they're going to have to move on, but they can afford to procrastinate a little, and the ARM ( the police force) has as a principal duty to eleminate all inventions with the potential for massive damage(which means almost everything; who can judge all the potential of an idea?) so technical development is slow.
But an awful lot of the "known space" stories (including of course "Ringworld") are wholy or partially set outside known space.
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