General objectives of the stage: The Library is the second stage of Run For Your Life mission. This is quite large area, which in addition is occupied by a very large group of policemen, on almost all difficulty levels. Your goal is to reach the exit located on the opposite end of the library.
Go down to the balcony below you, because you can't do anything from the starting position. If you play on one of lower difficulty level, you can feel pretty safe here and carefully plan next steps. But if you play on higher difficulty levels, you should take into account that soon a single opponent will appear here (screen above). You can wait until he walks away, sneak past behind him or stun/kill him, thus easily obtaining Chicago policeman disguise.
A balcony where you've started this stage can be left in two ways. The most obvious solution is to choose right stairs (screen above), but you can also go left and locate a place where you can jump down from a balcony. In both cases it is worth to wait until nearby policemen end conversation and spread away. "Only" three officers should remain then in the area.
As I mentioned earlier, your goal is to reach the opposite side of the library, but I would advise not to rush with that, especially that policemen paths often intersect with each other. Anyway I recommend looking around the starting place, finding two power cords (a nice replacement for garrote). There are also many levers in the library, as one shown on the above screen. You can use them to release large chandeliers to kill enemies standing beneath them or to distract them.
After initial exploration of the area, move towards your actual goal. I suggest bypassing a single officer standing on the right (screen above). Depending on your preferences you can leave policemen alone or kill/stun them and hide bodies in crates.
During walk through the library you should notice that policemen successfully restored the power. Fortunately it is only a temporary situation because after few moments the power will be cut off again. You can speed up this process by interacting with a fuse box shown on the above screen. This is also another good method to distract enemies.
There are several different paths leading to the opposite part of the library. You can of course use one of the main passages on the ground floor (careen above), although there are many policemen in the area and even on lower difficulty levels it might be hard to avoid them.
A better idea to get to the other side of the library is to use upper balconies. Depending on your preferences you can locate one of places, where you can catch the upper ledge or use a small stairs shown on the above screen, leading to the right balcony.