Imagine that a meteor strike wipes out the vast majority of living humans, leaving only a few thousand scattered individuals around the world. Naturally, civilization collapses, with only basic reading and arithmetic skills retained.
The survivors transmit a great deal of "lore" about the achievements of the past to their children, but the scarcity of specialists and the breakdown of communications and education result in this knowledge becoming increasingly vague. Newer generations have not experienced past civilization and they become increasingly doubtful about the stories they hear about "skyscrapers", "airplanes", "relativity", etc. As a result, knowledge becomes myth, and is increasingly forgotten or embellished with fantastical elements.
Centuries pass. Environmental conditions start to improve. The remnants of mankind emerge out of their hiding places. Almost everything has been lost, but the survivors have adapted, and our species is no longer in danger of immediate extinction.
One day, a young sheperd boy discovers the ruins of a great building that once housed a library. Almost nothing of the library's collection remains, save for an old briefcase left by some unfortunate visitor in the basement. The boy takes the briefcase to the elders of his village, who -after much effort- manage to open it, discovering that it contains five books, the first books to see daylight in over a thousand years.
If you were to magically insert any five books into that briefcase, which ones would you choose and why?
PS: I will give my own answer after I think about it for a day or two.
So, here is my list:
The New Testament. Almost all human civilization has had a religious aspect to it, and the religious imperative has spurred much discovery and exploration. The New Testament would provide a basic moral ideal around which society could function, and has functioned successfully in the past. It would also contain the imperative to spread the gospel around the world, which would help re-establish communication among different survivors.
The Elements by Euclid. Human beings could probably not understand most advanced mathematical subjects without a suitable education. The Elements would provide basic geometrical knowledge that is both practically useful, but also encompasses the entire mathematical process: axioms, reasoning, proofs.
The Republic by Plato. The Republic is a book of basic philosophy which covers and hints at many subjects. It can be read by a non expert easily, unlike most later philosophical works. Its main value would be to instruct people about the value of discussion and argumentation as a way to approach the truth. It would also teach people to value laws as a way to create a well-ordered society.
Gray's Anatomy of the Human Body, or some other anatomical text. This would help demystify the human body, and show that it is a well-working system which can be studied scientifically. Such a book would be a useful in medicine and biology, and it would spur people to investigate the inner workings of living things.
Any accessible book on modern cosmology. People should learn about our picture of the universe, even if they do not understand perfectly how it works. They should learn that the earth is round, that the moon is its satellite, that it orbits the sun, which is a star in a galaxy, one of many in an expanding universe with billions of other galaxies. Perhaps they will not believe it at first, but even if they take it as a myth, it will be better than other possible myths. It would also hint at the grandeur of the universe, and thus motivate them to learn about it.