In the comet/apocalypse classic Lucifer's Hammer, one of the survivors takes the effort to cache hundreds of books--individually sealed and then buried an a cleared out septic tank. They're books on a wide range of topics--science, industry, history--with the intent that they could be used to one day rebuild civilization.
No survivor should be without a library of useful books, be they military manuals and survival guides, technical manuals, religious texts, histories or more theoretical. They can teach useful skills and knowledge pre-collapse, and help with survival and rebuilding efforts if/when the collapse comes.
In this day and age of easily available internet info and digital readers, physical printed books are often overlooked. Unfortunately, in a collapse scenario, this information would quickly become unavailable. Good luck getting those how-to's on YouTube when the grid is down.
Printing could quickly become a valued skill post-collapse. Community bulletins, newsletters and updates could become a primary means of communication. Then there's of course the ability to copy other books and print new ones--the printing press is hailed as one of man's greatest achievements for a reason. Something to think about for those considering their role in an apocalyptic society.
A library of useful books could also become a source of barter and support--some books could become essentially priceless. Without the grid--computers, TV, movies--even B-grade novels would be highly valued as forms of diversion and escape.
I'm one of those who dislikes the massive clutter that comes with a large book collection, so the siren's call of digital readers is sweet to me. An eReader like a Kindle powered by a solar set up is a potential option, and a heck of a lot more mobile than a library of a couple thousand books. Unfortunately, they're prone to damage, breaking, etc. We have printed books that are centuries old--let's see your Kindle last that long.
What are some of your must-have books for after the fall of civilization? What's your strategy--are you focused on a single topic of interest (woodlands survival, blacksmithing, medical, etc.) or more widely spread?