After completing Horror from the Deep, you are rewarded with a damaged book of your choice: either Saradomin, Guthix, or Zamorak. You do not need to complete your first damaged book before obtaining a new one of a different type from Jossik. 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.
Unfinished books also count as God items in the God Wars Dungeon. You can see which God your book represents by examining it.