It was the Elves of Eregion who made all the rings, except for the One which Sauron forged by himself in Mount Doom.

After the defeat of Morgoth in the First Age, some of the remaining Noldorin Elves settled in Eregion and built a city called Ost-in-Edhil around the year 750 in the Second Age close to the west gate of the dwarven kingdom of Moria. About the year 1200, Sauron came among the Elves in a fair form using the name Annatar (Lord of Gifts), but with a dark plan to ensnare them. Sauron greatly desired to "persuade the Elves to his service, for he knew that the Firstborn had the greater power [The Silmarillion]." He taught them secret lore, and with this knowledge their craftsmen (a guild called the Gwaith-i-Mírdain, the People of the Jewel-smiths) created the Rings of Power which included the Seven and the Nine. But Sauron had a part in the creation of these rings and he guided the Elves in their making. However, the Three Elven Rings were conceived and made by the Elven-smith, Celebrimbor, alone, and Sauron never touched the Three.