The current world will not end in a bang like some 2012 maya pipe dream, killing computers overnight. What we have at hands right now is the ongoing process of choosing by inaction not to create enough ways to harvest renewable energy. As the fossils run out, we will see a gradual shift away from our current global industrial world.
Cheap mass shipping to the other side of the world will be among the first luxuries to go, meaning we will need to start to produce most of our goods locally again, starting from the basics and working up to more complicated ones. Which is where the library kicks in. If we reasonably manage our inheritance from the industrial era, we will have quite a stretch of time available while which we can rig up a some power to a computer to read and transcribe the library. I mean, many a slashdotter will be able to rip apart that electric car into some wind generators, batteries included.
Now we can plot a simple graph with two lines - one of us exhausting and repurposing our current goods and infrastructure until we run out, the other line being us rebuilding our civilization on renewable and sustainable production and goods. What is still undecided is how low the valley will go, and whether we hit such a critical low of development that we will never come back up again.
How well this will go depends on a few factors. First, practicing any technology needs a society able to feed specialists. This ability will decline sharply everywhere, because our current agriculture is 100% about converting oil into food - there is a real possibility that billions will die of hunger. Second, some countries like the USA and GB will have to start pretty much from the beginning, having destroyed their industrial base through corporate looting and offshoring. Contrast that with China or Germany with their massive industrial base which only needs to get the power back on. Third is of course the availability of raw materials, on which point do also note the lack of plastics in a post-oil world.
And if this was too easy, expect mass migrations caused by sea level rises, thirst and hunger and wars of every size and reason to complicate matters further. Only a state with can comfortably secure it's territory, food and resources with a reasonable surplus will have a chance to actually think about a rebound. At this point we can only hope there will be one.
Or we could get off our collective arses and actually do something about the future. I seriously doubt we will see an actual global push into renewable and sustainable, though. This would require effort, resilience and actual change, all of which are in a very short supply on this scale; furthermore, it would mean replacing our power structures, ideologies and economical systems, all of which are and will fight tooth and nail to survive. So it remains that the next best thing is for us to compile some kind of a library of survival knowledge...