The fictional language commonly called the language of the Elves in J.R.R. Tolkien’s writings is Quenya.
Quenya is one of Tolkien’s most developed Elvish languages. He based aspects of its sound and structure on languages including Finnish, while creating its vocabulary and grammar as part of the larger linguistic history of Middle-earth. In Tolkien’s mythology, Quenya is associated especially with the High Elves and with the ancient realms of Valinor.
Quenya is not simply a universal Elvish language. Tolkien also created Sindarin, another major Elvish tongue that is more commonly spoken by many Elves in the events of The Lord of the Rings. Khuzdul is the language of the Dwarves, and the Black Speech was created by Sauron. The distinction between Quenya and Sindarin is a frequent source of confusion.