The Elves of Valinor primarily spoke Quenya in J.R.R. Tolkien’s mythology.
Quenya is one of Tolkien’s best-developed invented languages. It is associated especially with the Ñoldor and Vanyar, Elvish peoples who lived in Valinor. Tolkien based aspects of its sound and structure on Finnish, while also drawing on other languages and his own historical-linguistic interests.
After the Ñoldor returned to Middle-earth, Sindarin became more widely used there, while Quenya acquired a formal and literary status. This distinction is why characters in Tolkien’s stories can have names or titles in both languages. For example, the name Galadriel is commonly connected with Sindarin, while many royal and ceremonial names are Quenya.
Quenya is not simply “the Elvish language” in every context. Sindarin is another major Elvish language, especially important in later Middle-earth. Khuzdul belongs to the Dwarves, and Black Speech was created for servants of Mordor.