2. How the Ring Came to Be and Its Early History
The Gwaith-i-Mirdain were the Elvish Jewel-smiths. They dwelt in Eregion, west of the Misty Mountains and established their realm at the end of the First Age, after the Breaking of Thangorodrim and the
Drowning of Beleriand. They were the most highly skilled of the Elvish craftsmen, with the exception of Feanor himself. The most skillful of the Gwaith-i-Mirdain was Celebrimbor son of Curufin.
After the fall of Morgoth, Sauron assumed a pleasing appearance and humbled himself before Eonwe, the herald of Manwe. However, Eonwe did not have the authority to pardon him and summoned him to Aman
where he might be judged by Manwe. Sauron was not willing to submit to such humiliation. He hid in Middle-earth and fell back into his evil ways.
After many years, Sauron's influence became manifest. He felt that the Valar had forgotten Middle-earth after the fall of Morgoth and the destruction that had been wreaked. He began to bring the Men of
the East under his evil sway, and, indeed, of all the peoples of Middle-earth, Men were the easiest to corrupt. Elves were more powerful and more resistant to temptation, and it was the Elves whom Sauron
wished to bring into his service. He avoided Lindon where Elrond and Gil-Galad dwelt. They doubted the fair shape which Sauron had assumed and they would not admit him to their lands. But they did not
know for a fact that the person who described himself as Atannar, the Lord of Gifts, was, in reality, Sauron. Elrond and Gil-Galad sent messages to the other Elves of Middle-earth urging them to beware
of Atannar, but their counsel was not heeded. Sauron persuaded the Elves that it was his desire to labour for the good of Middle-earth, observing that it had been left desolate and dark. The Noldor of
Eregion were receptive to Sauron's suggestions. They wanted to increase their knowledge and skill and to recapture the bliss of the West to which they had refused to return.
In the city of Ost-in-Edhil in Eregion the Elves surpassed all that had been done before in the way of smith-craft and they made Rings of Power. In this they were guided by Sauron and he knew what they
did and he wished to bind the Elves to him. In secret he made One Ring to rule all the others ;
"and their power was bound up with it, to be subject wholly to it and to last only as long as it too should last. And much of the strength and will of Sauron passed into that One Ring; for the
power of the Elven Rings was very great, and that which should govern them must be a thing of surpassing potency; and Sauron forged it in the Mountain of Fire in the Land of Shadow. And while he wore
the One Ring he could perceive all the things that were done by means of the lesser rings, and he could see and govern the very thoughts of those that wore them."
The Elves became aware of Sauron's ploy as soon as he put the One Ring upon his finger. They took off their rings and three of them they saved - Narya, Nenya and Vilya - The Rings of Fire, Water and Air.
Their stones were respectively ruby, adamant and sapphire. They were the last three Elven Rings made by Celebrimbor. They were untouched and unsullied by Sauron and they possessed the greatest powers.
This raises an interesting inference. Sauron demanded that the Elves surrender all their rings to him. He claimed that the Elven-smiths could not have made them without his lore or counsel. Then the text
goes on  to say that the Three were saved. This suggests that there were more than the Three, and that in some way they were destroyed or lost.
In The Fellowship of the Ring  Gandalf says:
"In Eregion long ago many Elven-rings were made, magic rings as you call them, and they were, of course, of various kinds: some more potent and some less. The lesser rings were only essays in the
craft before it was full-grown, and to the Elven-smiths they were but trifles - yet still to my mind dangerous for mortals. But the Great Rings, the Rings of Power, they were perilous"
The first reference that Gandalf makes to the Three comes after he has spoken the verse and identified the One. "The Three, fairest of all, the Elf-lords hid from him, and his hand never touched them
or sullied them."
The relationship of the Three with the One is taken up by Elrond.
"..... and many eyes were turned to Elrond in fear and wonder as he told of the Elven-smiths of Eregion and their friendship with Moria, and their eagerness for knowledge, by which Sauron
ensnared them. For in that time he was not yet evil to behold, and they received his aid and grew mighty in craft, whereas he learned all their secrets, and betrayed them, and forged secretly in the
Mountain of Fire the One Ring to be their master. But Celebrimbor was aware of him, and hid the Three which he had made; and there was war, and the land was laid waste, and the gate of Moria was
I believe that it is fair to conclude from this that Celebrimbor and the Elven-smiths made more rings than just the Three. When Sauron donned the One, the Elves, hearing the fateful words spoken by Sauron
which were engraved on the Ring  and realising that Sauron could see and govern their thoughts, removed their Rings and lost or destroyed them. This conclusion is justified for there is no further
reference to the lesser rings being in existence. The Three Great Elven Rings, pure and untouched by Sauron, were hidden and retained by Gil-galad (and later Elrond), Cirdan (and later Gandalf) and
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The Tolkien Encyclopedia
The Art of Tolkien
One Ring to Rule Them All by David Harvey
Hypertextual System by FMI Publishing, 1995