In J.R.R. Tolkien’s legendarium, the Elves made the Rings of Power with Sauron’s instruction and influence.
The chief makers were the Elven-smiths of Eregion, led by Celebrimbor. Sauron, disguised as Annatar, taught them techniques of ring-making. The Elves forged the Three Rings independently of Sauron, while the Seven and the Nine were made with his involvement. Sauron secretly forged the One Ring to dominate the others.
The Dwarves received seven Rings, but they did not make the Rings of Power. Men received nine and were eventually transformed into the Nazgûl. The Three Elven Rings were named Vilya, Narya, and Nenya. Tolkien’s account places their creation in the Second Age, making the Rings part of a much older history than the events of The Hobbit or The Lord of the Rings.