It won't progress and I don't know if I haven't found a book or if its because its glitched

Wow. Two bug posts in one day for me. Here you go:

• If by some chance the guards have died prior to this quest (a dragon attack, for example), they may not respawn for the quest once it starts and thus will not ask for your invitation and will not unlock the door, preventing you from proceeding from the quest.
  
  • This bug is fixed by version 1.5 of the http://www.uesp.net/wiki/Skyrim:Patch.
• The http://www.uesp.net/wiki/Skyrim:Thalmor_Robes are supposed to function as a disguise, but this does not work, even as an Altmer. Despite having the same effect, MQ201ThalmorDisguise, only the http://www.uesp.net/wiki/Skyrim:Hooded_Thalmor_Robes work. You can obtain one from the wizard upstairs. It is also possible to smuggle these robes into the Embassy and use them as disguise.
  
• Sometimes the next quest will not be started after the completion of this quest.
  
  • This bug is fixed by version 1.5 of the http://www.uesp.net/wiki/Skyrim:Patch.
• Some quest related items will not be removed from your inventory when Delphine takes it. This includes weapons, such as Ulfric's War Axe
  
• When you meet Delphine at the stables, she may attack you. This may only occur if you have a bounty on your head.
  
  • The solution is to go back to Riverwood and talk to a guard, who will charge you with your crimes; you have to pay the fine and then return to the stables.
• If Etienne Rarnis dies before talking to him, the quest will not progress to the next stage. Reload if this happens.
  
• You may not be able to retrieve your equipment, as the chest will be empty.