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This is a guide to the second part of the Run For Your Life mission in Hitman: Absolution which is called Library. It describes how to complete this mission with the maximum score (excluding how to complete all the challenges in this area). This means playing on the purist difficulty, avoid being spotted and recovering the evidence in this area. Doing all this you will gain 19,200 score.
At the start drop down and make your way to the right side of the balcony. Take cover on the pillar so that you can't be seen from the platform at the top of the stairs. Wait for a police officer to come and once he has turned his back on you sneak up on him and subdue him. Take his outfit and hide the body in the cabinet nearby. Go down the stairs and take cover on the book shelf at the bottom of the stairs.
Wait for the police officer ahead to have turned his back on you, then get out of cover and sneak past behind him. Keep going underneath the stairs. Go up the stairs to the left and follow the balcony leftwards at the top of the stairs. Eventually you will get to a gap in the railing. Drop down and turn left and go towards the radio sitting on the table ahead. Throw it behind the police officer looking down on a table and talking to another police officer.
Once the police officer is distracted sneak up behind the other police officer. The evidence is on the table underneath the statue behind the other police officer.
Go back out of the area through the other gap in the same lined up row of tables as you entered through. Go towards the door in the wall ahead, staying between two rows of tables. Once you have gone through the wall take cover on the bench nearest you.
If there isn't a police officer directly looking at the gap change cover immediately. Otherwise wait for the police officer to leave. The same is true for the next gap. Before you go on check that there isn't a police officer further down the rows of book shelves to the right of the cover. If there is, wait for him to go out of sight. Otherwise follow the isle until you get to some stairs and go up the stairs. At the top turn around and go between the wall and the railing towards the police officer standing in front of the door. You can just sneak by behind him.
Keep following the platform around until you can jump up to a ledge. Climb up and follow that platform until you can walk over a beam. On the other side the exit is just to the left. Once you have gone through it, it is the end of this part of the mission.