The Tengwar are an artificial script which was invented by J. R. R. Tolkien. In his works, the Tengwar script, supposedly invented by Fëanor, was used to write a number of the languages of Middle-earth, including Quenya and Sindarin. However, it can also be used to write other languages, such as English (most of Tolkien's tengwar samples we know of are actually in English). The word tengwar is Quenya for "letters". The corresponding singular is tengwa, "letter".
The sarati, described in Parma Eldalamberon 13, a script developed by J. R. R. Tolkien in the late 1910s, anticipates many features of the tengwar, especially the vowel representation by diacritics (which is found in many tengwar varieties), different tengwar shapes and a few correspondances between sound features and letter shape features (though inconsistent).
The tengwar were probably developed in the late 1920s or in the early 1930s. The Lonely Mountain Jar Inscription, the first published tengwar sample, dates to 1937 (The Hobbit, most editions). The full explanation of the tengwar was published in Appendix E of The Lord of the Rings in 1955.