In the previous chapter, Alduin's Wall, You, Esbern, and Delphine went to the hidden Blades Stronghold of Sky Haven Temple in Karthspire, and found Alduin's Wall inside. It showed that Alduin was defeated in the past by some kind of shout.

With Esbern's help, I've deciphered Alduin's Wall in Sky Haven Temple. It revealed that Alduin was defeated in ancient times by a shout of some kind. Maybe the Greybeards can teach me this Shout, or at least tell me how I can learn it.

Talk to Arngeir

Climb up the stairs behind Alduins Wall, and exit through one of the doors to Skyrim. Fast Travel to High Hrothgar (Unless you want to walk all those 7,000 stairs again) and locate Arngeir inside. Tell him you need to learn the shout used to defeat Alduin. He will ask you where you learned of that and who you have been talking to. Tell him it was recorded on Alduin's wall. He will be upset at you and at the Blades. He thinks the Blades are making you stray from the path of Wisdom, using the Dragonborn as a puppet for their interests. Tell him you want to defeat Alduin, ask him if he does not. He will say maybe Alduin is not meant to be defeated, perhaps the world is supposed to get destroyed, and then reborn. Ask him if he won't help you than. He will say that no, not until you return to the path of Wisdom.

Master Einrath will suddenly show up and speak to Arngeir something in Dragon Tongue. He sounds furious. Arngeir will then turn to you and say that he changed his mind, he will help you. The decision whether or not to help is not his to make. Ask him if he will teach you the shout than. He will say he cannot teach it to you because he does not know it. It's called Dragonrend but he does not know the words for it. Tell him you thought he knew all the words of power. He will tell you that the knowledge of that shout was lost before history began. Ask him what is so bad about Dragonrend. He will say it was created by people who lived under the cruelty of Alduin and the dragons and has evil imbued in it.

Ask Arngeir how you can defeat Alduin if that shout is lost. He will tell you that only Paarthurnax, the master of their order, can answer that. Ask him who is Paarthurnax. He will tell you that Paarthurnax is their leader. Ask him why haven't you met him yet.  He will tell you he lives in seclusion on the very peak of the mountain. Ask him how  you can get to the top of the mountain to see him. He will tell you that only those whose voice is strong can find the path. They will teach you a shout to help you find the way to Paarthurnax.

Your quest log is updated:
"Arngeir knew the name of the shout, "Dragonrend",  but could not teach it to me. However, he has agreed to show me the way to reach Paarthurnax, the Greybeards' Leader, who lives at the top of the throat of the world. Arngeir says that Paarthurnax is the only one who may know this Dragonrend shout."

Follow Arngeir.into the High Hrothgar Courtyard. Your objective now is to learn the "Clear Skies" Shout. Step on the runes in the ground to absorb the words. You will learn the following words of power:
Sky, Clear Skies
Spring, Clear Skies
Summer, Clear Skies

After learning the words of power, your objective is to use the "Clear Skies" shout to open the path. Bring up your magic menu and equip the clear skies shout. Climb the stairs to the Southeast. There is lots of fog and mist there which prevents you from advancing. Use the new shout to dissipate the fog and open the path. Your goal now is to speak to Paarthurnax.

Continue making your way Southeast along the path, using the clear skies shout to dissipate any additional fog. Cross the bridge. Fight the Ice Wraiths along the way. After a long climb, you will reach the throat of the world.

Paarthurnax will show up with  a loud roar. He is a dragon. He will ask you what brings you to his mountain. Tell him you were not expecting him to be a dragon. He will ask you why are you intruding on his meditation. Tell him you need to learn the Dragonrend shout and ask him if he can teach you first. He will tell you to have patience, and that there are formalities that need to be observed at the first meeting of two of the Dovahkiin. The elder speaks first. He will breath fire and ask you to match it. Your goal now is to learn the word of power from Paarthurnax. Go to the runes and learn the word of power Fire, Fire Breath. Use your new Fire Breath shout on Paarthurnax.

Talk to Paarthurnax. Ask him to teach you the Dragonrend shout. He knows you seek a weapon against Alduin. Ask him how he knew you come for Dragonrend. He will say Alduin and Dovahkiin return together. But he does not know the shout you seek. Mortals created it as a weapon against the dov, the dragons. Their minds cannot even comprehend its concepts. Ask him how you can learn it. He asks you why you want to learn this Thu'um. Tell him you need to stop Alduin. He will insist, why must you stop him. Tell him the prophecy says that only the Dragonborn can stop him.

He will tell you, just because of the prophecy, it doesnt mean you should do it, and asks you whether you are just a puppet of destiny, afraid of fate. Tell him that what better reason to act than to fulfill your destiny. He will remind you that Alduin also follows his destiny as he sees it.  He will ask you if you know why he lives here in the throat of the world. Tell him you never thought of this. He will tell you this is the most sacred mountain in Skyrim. Here, the masters of the voice brought Alduin to battle and defeated him. Ask him if that was using the Dragonrend shout. He will say Yes and No. Alduin was not truly defeated, otherwise you would not be here today seeking to defeat him. The Nords used the shout to cripple Alduin but this was not enough. The Elder Scroll was what was used to cast him adrift on the currents of time. Ask him if the ancient Nnords sent Alduin forward in time. He will say it wasn't intentional, they hoped he would be gone forever.

Ask him what an Elder Scroll is. He will say it is an artifact from outside time. It does not exist but it has always existed. Elder Scrolls have been used for prophecy. Your prophecy comes from an Elder Scroll. Ask him how any of this helps you. He will tell you that time was shattered here because of what the ancient nords did to Alduin. If you brought the Elder Scroll here, to the time wound, you would be able to go back in time and learn dragonrend from those who created it. Ask him if he knows where to find an Elder Scroll. He says that you are probably better informed then him. Tell him the Lorekeeper at the college of winterhold might know.

If you ask him what the Dragonrend shout actually does, he says he cannot tell you in detail since he never heard it in use. It was the first shout created solely by mortals. It forces the dragon to experience the concept of Mortality.

Ask him if other Greybeards come there to train since he is the master. He will tell you he has taught the voice for centuries, but others have not come there for centuries, you are the first one.

Ask him how could an Elder Scroll cast Alduin through time. He will say they erased the knowing of it from time itself. Dragons are attuned to the flow of time and vulnerable to it.

Ask Paarthurnax what to do with the Elder Scroll when you find it. He will tell you to return it here, and then nothing is certain. You will see his friends, Hakon, Gormlaith, Felldir. Ask him who they are. They are the first mortals taught the shouts, the leaders of the rebellion against Alduin.

This completes the quest "The Throat of the World" and starts the next main quest, "Elder Knowledge"