The script created by Fëanor for Tolkien’s Elvish writing is Tengwar.
In Tolkien’s fictional history, Fëanor devised the Tengwar in the First Age. The script was designed to represent speech sounds efficiently and was later adapted for several languages of Middle-earth, including Quenya and Sindarin.
Tengwar is a writing system rather than a language. This distinction is a common source of confusion: Quenya and Sindarin are languages, while Tengwar is the script used to write them. Tolkien also created different modes of Tengwar for different languages and pronunciation systems.
The script appears in illustrations, inscriptions, and title pages associated with Tolkien’s works. The Ring-inscription shown in The Lord of the Rings is a famous example of Tengwar writing, although the words themselves are in the Black Speech of Mordor rather than an Elvish language.