Paarthurnax (Quest)

Background
Delphine and Esbern have learned of Paarthurnax's position as leader of the Greybeards. They inform the Dragonborn of Paarthurnax's role as Alduin's second-in-command during the Dragon War and his responsibility for the atrocities committed. Bound by their oaths as Blades, they cannot offer the Dragonborn further assistance until Paarthurnax is slain. This quest is optional; it does not need to be completed in order to finish the main quest.

Overview
This quest is purely optional. In order to continue Blades storyline, it must be completed before the conclusion of the Main Quest. However, doing so will prevent any further communication with the Greybeards, including the radiant quest to locate Words of Power. Players who decide to kill Paarthurnax, however, receive a different conclusion to the main storyline.

Killing Paarthurnax
He should be very easy compared to Alduin. Dragonbane is useful here as always. Dragonrend will bring Paarthurnax to the ground, and Fire Breath is useful for damaging Paarthurnax.

How NOT to kill Paarthurnax (PC only)
It is possible to complete this quest without needing to slay Paarthurnax by using command: setstage MQPaarthurnax 100 This way, Paarthurnax will remain alive, the Greybeards will still be hospitable and the Blades will talk once more.

There are also mods available to bypass this quest or the player could use the console command (setessential  0) and kill the Blades instead.

Trivia

 * Speaking to Arngeir regarding the Blades' request, he will tell the Dragonborn about Paarthurnax's reason for siding with Alduin and later, his rebellion which brought to Alduin's first demise. There is the option to tell Arngeir, Paarthurnax must die or that he is going to be spared. This will affect the conversation between Esbern and Arngeir if in Season Unending, during the negotiation of a treaty.
 * Should the Civil War questline be complete (thus bypassing Season Unending) and the player proceeds directly to the endgame, Delphine and Esbern will remain in Sky Haven Temple. However, they remain in disapproval and the quest disappears from the log.
 * There is no actual way of denying the request of the Blades, other than console commands/mods on the PC.
 * Without Arngeir, it is still possible to get radiant quests for words of power by shouting in a town and waiting for a Letter from a Friend.
 * This quest is still possible to complete after completing Season Unending by depleting all of Paarthurnax's health then quickly fast traveling to Sky Haven Temple.
 * It is possible to kill Paarthurnax directly after the quest, Alduin's Bane, since he is no longer an essential character. Once he is dead, travel to Sky Haven Temple and talk to Esbern. He will introduce the Dragonborn to the quest to kill Paarthurnax, but you can tell him Paarthurnax is already dead. (Also, this will NOT interfere with the Peace Treaty mission at High Hrothgar later).

Bugs
Партурнакс (Квест) Paarthurnax (Quest) Paarthurnax (Misión) Paarthurnax (Missione)