Walkthrough: Enter the library and wait for one of the allied soldiers to join you after he's left the main gate #1. You won't have to be in a lot of hurry here, however you won't find any interesting items in the vicinity. You should only examine one body #2 in hopes of collecting extra ammunition.
Use the stairs to get to the upper balconies #1 and notice that you won't be allowed to use the main gate to reach the next area. Instead turn right and proceed towards a new corridor #2, collecting a gas mask filter along the way.
You'll have to be careful here, because you're going to be attacked by "tentacles" attached to the ceiling #1. The easiest way to avoid injuries is to stay away from them and to sprint often. You can examine a new body along the way #2, however you'll only find standard ammunition.
Proceed to the right where you'll have to go through a second corridor filled with tentacles #1. The rules are the same, so you'll have to start running and prevent the main character from moving too close to the tentacles. Examine a new body and then head through a small hole in the wall #2 (you'll have to press the crouch key).
Once you're inside you should find a new body. Approach a small hole in the nearest door #1 and choose one of the weapons from your inventory. You'll have to fire a single bullet to destroy a wooden beam blocking the main gate. Wait until your allies have gained access to the next area and they will soon get you out of this room #2.
Find two other bodies. Be careful while standing near the window #1, because a flying demon may appear near your position. Use one of your guns to scare the creature away. Explore the surrounding area and you'll find a new damaged door #2.
In this case you won't have to aim for anything in particular, because you'll want to destroy an entire door #1. Don't waste your ammunition, because you'll be allowed to do this using only a knife. Collect supplies from a new body and then locate a hole in a nearby wall #2.
Crawl through the hole to find yourself standing inside a much bigger room. Explore the area to locate two new bodies and then move on with the mission by firing at a chandelier found close to the ceiling #1. Wait for this object to break down a nearby door #2. You can now use the stairs to get to the next room along with the rest of your team.
Get ready, because you're about to take part in a battle with a flying demon #1. Generally you shouldn't be wasting your ammo here, especially since you won't be able to prevent the beast from grabbing one of your colleagues and then leaving the building. Listen to new orders and choose a passageway leading to the upper balconies #2.
After you've made your way to the top you should proceed to your left #1. Search the area to find shotgun ammunition and then choose a passageway located nearby. Eventually you'll have to find a new closed door and use a knife or a standard weapon to destroy it #2. Entering the next room will allow you to end this mission.