Short answers, pulled from the story.
Tengwar was created by J. R. R. Tolkien, the author of The Lord of the Rings. Within his fictional world, the script was invented by the Elf Fëanor in Valinor. Tolkien probably developed the actual script in the late 1920s or early 1930s.
Tengwar was first used to write the Elvish languages Quenya and Telerin. It was later used for Sindarin and many other constructed languages in Tolkien's world. Tolkien also frequently used Tengwar to write English.
The first published Tengwar sample was the Lonely Mountain Jar Inscription, which dates to 1937. The full explanation of the Tengwar system appeared in Appendix E of The Lord of the Rings in 1955.
Each Tengwar letter encodes phonetic information through its shape. The columns of the system correspond to places of articulation, such as dental, labial, and velar sounds, while the rows correspond to manners of articulation, such as voiceless stops, fricatives, and nasals. Transformations like doubling the bow or raising the stem apply consistently across the entire alphabet.
A Tengwar mode is a specific orthography for writing a particular language in the script. Some modes use diacritical marks called tehtar for vowels, while others, like the mode of Beleriand seen on the Doors of Durin, write vowels as full letters. Fans and scholars have created modes for many languages including English, Spanish, German, and Welsh.
Tengwar is not part of the official Unicode standard. Michael Everson made a proposal for Unicode inclusion in 1997, and a range was tentatively allocated in the 2023 Unicode roadmap, but that allocation has since been removed. The unofficial ConScript Unicode Registry assigns Tengwar to the Private Use Area range U+E000 through U+E07F.
With the exception of John Rhys-Davies, all the actors who played members of the Fellowship of the Ring in The Lord of the Rings film trilogy have Tengwar tattoos of the English word 'nine'. Footballers Sergio Agüero and Fernando Torres have their first names written in Tengwar tattooed on their forearms.