Not when the only survivors are armed wingnuts who clean out all with the presence of mind to be survivalists in a non violent way. The last place they will go is a library.
David Brin made an interesting observation in his novel "The Postman". The internal narrative of the hero, a former history teacher, that was half the point of the book! The movie may have lacked all that, and because I liked the book I didn't want to watch Kevin Kostner mess up another post-apocalyptic story like he did in Waterworld.
Anyway, the observation? A fully armed, tinned-food and ammo kind of survivalist would quickly try and find out where the other fully armed survivalists are and take them out. After all, they're the main threat aren't they?
The winners are communities. We know specialisation is a thing, that certain people are wired to more efficiently do certain jobs. Communities thrive. Lone survivalists might survive - but do they thrive? They're all alone living off borrowed time. Communities are putting back into their local environment, their farms, their soil, and gradually building up a knowledge base to move forward. Eco-survivalists like those peak-oilers at
Homepage - Resilience see community as key. I think sheer self-interest would see educated middle class types immediately trying to push for community, for co-operation that benefits all, over the thuggish self-interest of the moment of the lone survivalist. Planning and forethought and ideals, over selfish short term gain. The Printers of the
Book of Eli verses the town mayor failing to run a civilised community. Rick from
Walking Dead, as opposed to all the 'Road Warriors' he bumps off along the way.
Once they got a community going, what technical hurdles would they face? In some ways their next 'industrial revolution' would be much faster than the first industrial revolution, as we have already learned the laws of physics and chemistry and biology that make the modern world possible. The mechanics and techs from the village would wait a while before exploring radioactive bombed out cities. Once safe, the salvage crews might rig a few horses up to whatever trailer is lying around (hollowed out school bus? Truck trailer?) and take their rations, plenty of drinking water, and go spend a week or so working through the local bombed out city. They're looking for energy systems like wind turbines, solar panels, and the tools and solder and kit that make them work. They're looking for tinned food and ammo that isn't too old or expired. For excess fuel and wood, for whatever helps build their community.
Crucially, they're looking for books, for something just to read for entertainment - never forget the value of entertainment at the end of the world when everything is so quite and boring! But also for engineering manuals that have instructions for future projects. Once their village has food supply issues sorted, they've got a lot more time on their hands now that there are no new TV shows to watch. Night time hobbies around candles quickly become night time hobbies around solar battery powered lamps. Things improve as they continue to scavenge and salvage. One thing they could have ample of, lying around, that the first industrial revolution didn't have is metal. Even farm belts would have heaps of useless cars scattered around, and it could be ample for years to come.
They'd get things up and running eventually, even if the local workshop had to stop working on cloudy days because their solar panels maxed out.
Smart survivalists might have seen the war coming and downloaded and printed out this "Civilisation starter kit" to have some knowledge to trade.
Machines : Index | Open Source Ecology (It's a step by step guide on how to build the top 50 industrial tools that make the modern world possible, but out of spare parts you might find in a hardware store or salvage from a factory.) But if not, other places will have their technical people dig up and study old manuals (by candlelight?) in the evenings as what else are you going to do in a barely powered Amish lifestyle wishing for better things? They'll research that next component to salvage for their next project.
Bit by bit society would build up again, but in a more walkable, human based city plan. Energy would be more valuable and prioritised for the most important survival and salvaging efforts. That is, until finally someone gets the nukes started again. Once they get breeder reactors up and running, any nuclear waste in that country becomes an incredible asset that could power the nation for centuries to come.
), I think we'd dig through buried libraries and salvage stuff and get back to the modern world within a generation or 2. 50 years tops? 
