Technically the main quest would be the one to defeat alduin, that starts with you going to whiterun and talking to the grey-beards, but others have considered it to be the civil war.
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In the game, and the official guide, the main strand is the one in which you take down Alduin - the Civil War strand is a side questline, along with the colleges/guilds/daedric strands
It is part of the main quest. Delphine will give you this mission.
you can't you're dragonborn
If you create a new character, you can repeat the main quest.
The closest you get is a shout which can summon a dragon who has allied with you, this happens during the main quest.
You have to complete main quest: dragon rising
Play the main quest line. At one point you learn the shout to summon a dragon.
It is not a quest reward as such, but you have to complete the main storyline quest Alduin's Wall before you can access it. It is there for the taking, should you wish to steal it (it is an owned item).
The end of the main quest features the king dragon Alduin being defeated by the Dragonborn, although the game can still continue after.
To fix the no quest items bug in Skyrim you have to download the most recent patch.
After you complete the main quest line you are rewarded with the shout "Call of Valor" which lets you summon one from a choice of three heroes, the three that aided you in the final battle.
The EVIL way.
Yes, however, you will have to complete the Main Quest to a certain stage, because the Elder Scroll from the Main Quest is later used in Dawnguard.