All Hail The King & Anarchy in the Library
After dealing with Krokus, he sends you off to speak with the Goblin King.
Head to the quest markere to find the King and speak to him. You may do the other quests in this area if you wish to do so.
Speak to the King and if you want to do things peacefully, there is no need to flatter him and just be direct. He might take offense with some words you may say.
(You can fight him for the book but it doesn't seem to be of any use. You may get his weapon as well but it isn't so phenomenal to kill a poor old Goblin King for.)
Speaking to him will reveal that there is a suspected plot against him and he wants you to find out who is behind this.
You can speak to the other goblins, but just go straight to the quest goal, Grogan.
Speak to him and ask him about the plot against the king. Unlike the others (if you have spoken to them) he will seem jumpy about the idea and demand that you leave.
If you go into Query Mode, you will see that he has an odd "Secret" stash. You can't access this while he is around so utilize the stealing mechanic in this game and wait for him to wander far.
When he is outside his walls, go ahead and swipe the Secret Plans from his secret stash.
Report your findings to the king and he will be glad to know who was plotting behind him. He gives you the book and completes this quest.