The two definitive early post-apocalyptic sci-fi novels are:
Star Man's Son (aka Daybreak 2250) by Andre Norton
A Canticle for Leibowitz by Walter M. Miller, Jr.
Other good examples are:
The Postman by David Brin
Lucifer's Hammer by Jerry Pournelle and Larry Niven
Alas, Babylon by Pat Frank (not really sci-fi)
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