It's 2100. About 50 years ago, modern civilization collapsed after a decade of turmoil caused by the depletion of oil reserves, pollution, global warming, erosion of arable land, increasing military strife over the remaining resources. Masses of people fled starvation, conflict anywhere resembling safety, and increasingly hostile environment, mainly by foot, and the majority didn't get too far. At some point, nuclear weapons entered the picture, but they were mainly used against choice targets in great powers; most of the large cities didn't need much outside help in dying and collapsed in disease, struggle for survival and survivors fleeing for countryside.

Global population has fallen by at least 90%. There's been enough time for the surplus population to die off and for nature and civilisation to recover a bit from the shockwaves. While the trauma to collective mind and loss of life has been enormous, society has established itself where it can and the circumstances, while still harsh, have stabilised a bit.

Fossile fuels, save for possibly coal, are not widely available. Forests, while depleted, are, as are remnants of old power plants etc.

To what extent and what kind of energy infrastructure could you run in those circumstances? I'm assuming you couldn't really use modern wind or solar power due to lack of rare metals needed in maintaining them, but could you use/modify/maintain hydropower plants or make use of coal, firewood or some other resource to run some kind of industrial base?

Keep in mind that there has been quite serious a loss of knowledge and experience in multiple fields, and the majority of people are employed in agriculture now. Experts, while they exist, are rare and usually not as well read as their modern equivalents. Petroleum is absolutely not an option.

Could you run a small clothing factory for example with that alone? Even produce some steam boats, or anything like a mining industry with basic railroads?

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    $\begingroup$ "Except possibly coal":" There is plenty of coal on Earth, enough to last for many many centuries. There will always be coal. Iron and coal are so plentiful on Earth, so 19th century technology will always be available.Now, *where exactly will that coal be, that may be a problem. Surprisingly, I cannot see how we could possibly run out of petroleum in 30 years; there is lots of the stuff available. Hydropower will always be available, obviously. Books live happily in whatever house is good is enough for people. But the last paragraph is the clicker: barbarians are barbaric. $\endgroup$ – AlexP Jan 21 '18 at 20:19
  • $\begingroup$ @AlexP: The problem is not running out of coal (or other fossil fuels), it's that if it's all burned, we run out of habitable biosphere. $\endgroup$ – jamesqf Jan 21 '18 at 20:21
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    $\begingroup$ Not running out of oil, but running out of oil that can be reached easily enough to make it economically feasible. Peak oil scenario, really, along with other disasters, and once complex systems start failing, I'd expect them to fail spectacularly. $\endgroup$ – VTu Jan 21 '18 at 20:25
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    $\begingroup$ @jamesqf: The question posits a nuclear war and a human population reduced to 10% of what it is now. Under such conditions global warming won't be a significant problem for a very very long time. $\endgroup$ – AlexP Jan 21 '18 at 20:30
  • $\begingroup$ Welcome to Worldbuilding! That's a lot of questions you've asked, so it might help you to get better answers if you split this post up into multiple posts asking each (specific) question in a single post, linking each post $\endgroup$ – Mithrandir24601 Jan 21 '18 at 20:31