Eru Ilúvatar

Eru (the One), also called Ilúvatar (the All High or the Father of All as defined in the index of name elements in The Silmarillion), is the name in the legendarium of J.R.R. Tolkien for the supreme God. He is the single omnipotent creator, but has delegated most direct action within Eä to the Ainur, including the shaping of the Earth (Arda) itself. Eru is an important part of the stories of The Silmarillion but is not mentioned by name in Tolkien's most famous works, The Hobbit and The Lord of the Rings (He is alluded to as "the One" in the part of LotR's Appendix A that speaks of the downfall of Númenor).

Eru as Creator God
Elves and Men were created by Eru directly, without delegation to the Ainur, and they are therefore called "Children of Ilúvatar" (Eruhini), and are thus the equals of the Ainur. The Dwarves were "adopted" by Eru in the sense that they were created by Aulë but given sapience by Eru. Animals and plants were probably fashioned by Ainur after themes set out by Eru in the Music of the Ainur, although this is questionable in cases where animals exhibit sapience, as in the case of Huan, or the Eagles in the Lord of the Rings and The Hobbit. There is a case to be made that the Eagles of Manwë are actually Maiar. Also, as Huan was initially a Hound of Oromë, and was able to overcome Sauron (himself a Maia), it is possible that he too was one of the Maiar. Another possibility is that Huan's sentience represents the limits of the gifts of the Valar to creatures, endowing them with purpose and cleverness that may nevertheless be something other than true sapience in the sense of independent existence before Eru. Melkor, after all, was able to instill some semblance of free will into his mockeries of Eru Ilúvatar's creations (Orcs, Dragons, Trolls) which surely were not authorized or "adopted" by Ilúvatar. While Orcs were ruined Elves, and thus derived from the initial Children of Ilúvatar (as can be seen in, for example, their apparently indefinite lifespan), the other races mentioned -- particularly Dragons -- seem to lack this correspondence, or any particular connection with the Music of the Ainur, especially since the Valar themselves were shocked to encounter the first winged Dragon, Ancalagon the Black.

Tolkien on Eru
Tolkien understood Eru not as a "fictional deity" but as a name in a fictional language for the actual monotheistic God, although in a mythological or fictional context. In a draft of a letter of 1954 to Peter Hastings, manager of the Newman Bookshop (a Catholic bookshop in Oxford), Tolkien defended non-orthodox aspects as rightly within the scope of his mythos, as an exploration of the infinite "potential variety" of God (The Letters of J. R. R. Tolkien, No. 153). Regarding the possibility of reincarnation of Elves, Hastings had written:
 * God has not used that device in any of the creations of which we have knowledge, and it seems to me to be stepping beyond the position of a sub-creator to produce it as an actual working thing, because a sub-creator, when dealing with the relations between creator and created, should use those channels which he knows the creator to have used already

Tolkien's reply contains an explanation of his view of the relation of (divine) Creation to (human) sub-creation:
 * We differ entirely about the nature of the relation of sub-creation to Creation. I should have said that liberation "from the channels the creator is known to have used already" is the fundamental function of "sub-creation", a tribute to the infinity of His potential variety [...] I am not a metaphysician; but I should have thought it a curious metaphysic &mdash; there is not one but many, indeed potentially innumerable ones &mdash; that declared the channels known (in such a finite corner as we have any inkling of) to have been used, are the only possible ones, or efficacious, or possibly acceptable to and by Him!

Hastings had also criticised the description of Tom Bombadil by Goldberry: "He is", saying that this seemed to imply that Bombadil was God.

Tolkien replied to this:
 * As for Tom Bombadil, I really do think you are being too serious, besides missing the point. [...] You rather remind me of a Protestant relation who to me objected to the (modern) Catholic habit of calling priests Father, because the name father belonged only to the First Person.

Inspiration and development
The title the Father of All is thought by some to be borrowed from the god Odin in Norse mythology, though the New Testament also refers to God as the one God and Father of all. Tolkien, as a Catholic and a scholar of northern European mythology, was probably influenced by both sources. (The name itself is probably based on the Old Norse Alfóðr, a name for Odin, however.) As Tolkien was highly educated in Finnish mythology, it would be no surprise if the name of Ilúvatar were influenced by Ilmatar, Maid of Air, one of the primal spirits of creation.

It is to be noted that in earlier works of the legendarium the name Ilúvatar meant "Sky-father", but this etymology was dropped in favour of the newer meaning in later revisions. Ilúvatar was also the only name of God used in earlier versions &mdash; the name Eru first appeared in "The Annals of Aman", published in Morgoth's Ring, the tenth volume of The History of Middle-earth.