The damaged book is a book held in the shield slot that can be obtained for 5,000 coins from Jossik after completing Horror from the Deep. The four Armadyl pages can be added to upgrade it to the book of law, which gives a damage bonus.
After completing Horror from the Deep, you are rewarded with a damaged book of your choice: either Saradomin, Guthix, or Zamorak. You no longer need to complete your current damaged book before obtaining a new one of a different type from Jossik; all 6 different types may be bought for 5000 coins each. Dropping or destroying a damaged book and talking to Jossik results in him returning it to you.
You can check which pages are currently in your incomplete book with the "Check" option. Once you have filled the book, you cannot take the pages out.
