[Algester]

hmmm I had to brush through my DLed copy of SAO vol 10 heres what I'm getting with using teh_ping's trnaslated first part

Spoiler:

Kirito is some other hospital and the same nurse is still taking care of him

With the help of Koujirou Rinko, Asuna was able to find out where Kikouka is and asks about Kirito/Kazuto

Kikouka states what he is trying to do and this opens up the topic for Project Alicization and where Kirito is at that moment inside Underworld and in the real world

Back at Kirito's point of view he does what he does at best being a fighter and a badass protagonist ever since arriving at the second town Zekaria en route to Alice in Centoria

Asuna may have joined in Underworld to help Kirito (if according to the original web novel then this is possible)

Volume 10 ends with the top branch from the Gigas Cedar made into a black colored sword

so far thats what I can decipher awaiting volume 11
and this is where I'll be asking the question for what purpose does making an ultimate AI net Kikouka I mean we know the end result that Alice joins Kirito's Harem but why was she chosen to be the ultimate AI if its covered in volume 10 my understanding of Japanese is quite shallow still so it may take time for me to understand it all