This soundtrack is created by Daniel Rosenfeld (a.k.a. C418) and Lena Raine. All credit goes these two for expanding upon one of the most iconic music tracks in video game history. I do not own any music seen in the video. No copyright infringement intended.

Here are the time frames:

Concrete Halls 0:00
Warmth 4:13
Ballad of the Cats 8:12
Dead Voxel 12:48
So Below 17:44
Chrysopoeia 23:03
Rubedo 28:06
Pigstep 33:19