The Damaged Map is a quest in NIER . It is given to you by the blacksmith in the Village.
You need to search the library in the Village. Check the bookshelves on the second floor to find a Dirty Treasure Map. Take the map to the strange-things shopkeeper in Facade. To repair the map, the shopkeeper needs 3 machine oils, 3 eggplants, and 3 goat hides. The machine oils are dropped by the flying robots in the Junk Heap factory, but they're a rare drop. However this is the only way to obtain them. The eggplants can be bought at the Village and the goat hides are gotten from goats in the plains. After you have all the materials and after the shopkeeper has restored the map, speak with the blacksmith's wife. She will ask that you find the treasure on the map. Go see Popola first at the library. She will tell you it can be found in the Lost Shrine. Check all the rooms on the second floor of the Lost Shrine; one of them has a shiny object that turns out to be a Pile of Junk. Report back to the blacksmith's wife, who will give you an hair ornament in return. Sell it at the strange-thing shop in Facade to get a Gold Coin. Return to the blacksmith once again and trade the coin for the Marked Map. Go see Popola again at the library, then head over to the northern plains where the giant bridge starts (near the Aerie and Forest). Examine the glowing spot under the bridge remains to find the Labyrinth's Shout.