This is the second tale in the Book of Lost Tales.
Exists in two versions, a pencil draft on loose sheets followed by an inked version in a notebook. The second version is given in HoMe#I - The Book of Lost Tales part 1, with some quotes of the first version in the commentary.
Title of "Ainulindalë" is added.
Presented as a transcription or translation of a document written by Rúmil.
Story didn't change much, but there were extensive changes made to the wording, and a few additions were made to the text.
The story is now separated from the rest of the main narrative and becomes its own work.
Exists in two versions, a rough draft (A) and a fair copy (B). ("Ainulindalë" enters in the fair copy.) The fair copy is given in HoMe#V - The Lost Road and Other Writings, with some quotes of the first version in the commentary.
labeled by Tolkien as the "Round World Version"
Ilúvatar only shows the valar a vision of what their music created, and the Valar enter to find the world unshaped instead of fully formed.
An account of the first conflicts between Melkor and the other Valar is added, previously found elsewhere.
The Sun exists from the beginning, and the moon is created by Morgoth.
Arda is now only one part of the creation
Exists in a manuscript draft (now lost apart from a single torn sheet), and a typescript (C*), some excerpts of which are given in HoMe#X - Morgoth's Ring.
Flat world version again, Sun not in existence from the beginning
Most of the 1946 wording retained
‘written by Rúmil of Túna and was told to Ælfwine in Eressëa (as he records) by Pengoloð the Sage’
Exists as an extensive revision (C) made on top of and on the back of the 1930s fair copy (B), and as a careful illuminated manuscript (D) made from that which differs a bit towards the end. C, is given in full in HoMe#X - Morgoth's Ring., followed by some excerpts from D.
For more information, see the three volumes of The History of Middle-earth cited above, and also see the entry for "Ainulindalë" in Hammond & Scull's JRR Tolkien: Companion and Guide, where the subheading "History" contains an overview of the writing history.
And for an even better overview, see "The Origins of the Ainulindalë: The Present State of Research" by Michaël Devaux in The Silmarillion: Thirty Years On.
Early versions of the Ainulindale exist in HoME 1 and 5, with the final versions being discussed in 10. Unlike the Valaquenta (which was split off quite late) the Ainulindale existed as a separate work from an early stage, pre-LotR.