I can't seem to find the Aetherium Wars book anywhere to start the quest, and it's really disappointing, because it's my favorite quest.

I know it's supposed to be in the Bard's College. So I searched everywhere in the Bard's College and didn't fin it. I then joined the Bard's College, completing required tasks, and searched again, still not finding it.

I believe it is also supposed to be in the Palace of the Kings in Windhelm, and I searched all over there, too, but still can't find it.

Does anybody know somewhere I can definitely find it? Or another way to start the quest?

http://uesp.net/wiki/Skyrim:The_Aetherium_Wars

Direct link to the UESP page on the book.

Just as a FYI I equip the Aetherial crown with the steed stone and the ritual stone powers.

The best way is to read it at Dragonreach. The mage has a copy in his adjoining area to his study.

The book should be on the first bookshelf, stariaght ahead and to the right, when you enter the Bard's college, in the entance...Is it not there?

No, I looked EVERYWHERE in the Bard's College. Twice.

I haven't however checked in Dragonsreach. I didn't know there was a copy in there.

do you have Dawnguard installed and activated? pretty sure it requires Dawnguard

Yeah I have the Legendary Version and I looked it up and they activate themselves. I mean I have bits and pieces of them like vampires and lycans (sinding),... you know... hmm....

Maybe I have to reinstall them..

If you don't have any luck there, I have read that the quest can also be started by visiting Arkngthamz and talking to Katria. Arkngthamz is located SE of Markarth ,directly east of Valthume, and directly south of Reachwind Eyrie