The Hastur Mythos is a term coined by John Tynes to describe the Great Old One Hastur through his manifestation as the King in Yellow, though it can also be used to connote the more Hastur-centric versions of The Yellow Mythos in general.
The name Hastur reached The Cthulhu Mythos, a mythology constructed by August Derleth around the 'cosmic horror' works of H.P. Lovecraft, thanks to its borrowing by Lovecraft from Robert W. Chambers' The King In Yellow – wherein it had in turn been borrowed from its originator Ambrose Bierce. Although Lovecraft himself (and indeed Chambers before him) used the name with very little context, its subsequent appropriation by the expanding Cthulhu Mythos put an identity to this previously unexplained term, making it an ancient eldritch abomination. This effectively also welded the continuity of its earlier appearances into this wider Mythos.
Tynes, though, essentially suggests that the ideas presented by Derleth and by the Call of Cthulhu RPG of Hastur as little more than a big octopoid blob don't really do the source material provided by Chambers and Bierce much justice. Instead he offers a way of looking at the mythos far more in keeping with the surreal and personal madness of those earlier stories.
In Tynes' reimagining, Hastur is described as an impersonal force of the universe, entropy, which "assumes an individual role only in response to the entropy caused by human beings – our destruction gives it form, our violence gives it name, our screams give it a voice. It is no more of a deity than gravity is, no matter how many people worship and ascribe it a personality and an intelligence". The King In Yellow remains a "curious manifestation of Hastur". Carcosa is a "strange ghost-metropolis that consumes other cities whose vice and melancholy draw the grim feaster-city towards them". The Phantom of Truth determines "whether the city shall be consumed or not". Yhtill was a city once consumed by Carcosa, but the royal palace remains separate, across the lake, re-enacting the events recorded in The King In Yellow (The Play). Byakhee are the inhabitants of a city long ago absorbed by Carcosa.
This material was originally published in the Pagan Publishing magazine The Unspeakable Oath – and was later worked up in greater detail for the Delta Green RPG. The original work can, however, be found online courtesy of Pagan Publishing:
The Carcosa Mythos?
Just to clarify the difference – the 'Hastur Mythos' is a term used to look at Hastur in a different light, particularly through his claimed aspect as the King in Yellow. The subtle distinction between the Hastur Mythos and the Carcosa Mythos is that the latter aims to look at the original stories as being (potentially) independent from Hastur and presenting the King as a terrible god in his own right. However, much of these two separate angles offer identical viewpoints or draw similar conclusions; see Mythos (Definition).