Middle-earth is the name used for J. R. R. Tolkien's fictional ancient Earth where the stories in his legendarium take place. "Middle-earth" is a literal translation of the Old English term Middangeard, referring to this world, the habitable lands of men. Mythologically, the Endor continent became the Eurasian land-mass after the primitive Earth was transformed into the round world of today. Although Middle-earth's setting is often thought to be another world, Tolkien actually conceived it as a fictional period in our Earth's own past 6,000 to 7,000 years ago.
Sindarin is an artificial language (or conlang) developed by J. R. R. Tolkien. In Tolkien's mythos, it was the Elvish language most commonly spoken in Middle-earth in the Third Age. It was the language of the Sindar, those Teleri which had been left behind on the Great Journey of the Elves. It was derived from an earlier language called Common Telerin. When the Ñoldor came back to Middle-earth, they adopted the Sindarin language, although they believed their native Quenya more beautiful. Sindarin shared common roots with Quenya, and the two languages had many similar words. Sindarin was said to be more changeful than the older tongue, however, and there were a number of regional 'dialects' of the tongue. The Sindarin spoken in Doriath was said to be the highest and most noble form of the language.
Before the downfall, most of the Men of Númenor also spoke the language. Knowledge of it was kept in the Númenórean realm in exile Gondor, especially amongst the learned. Sindarin is the language referred to as the Elven-tongue in The Lord of the Rings.
Tolkien originally imagined that the language which would become Sindarin was spoken by the Ñoldor (second clan of Elves). However, Tolkien later decided that it was the language of the Sindar. For this reason it is called Noldorin in the older material, such as the Etymologies. When Noldorin became Sindarin, it also adopted some features of the originally unrelated language Ilkorin. Tolkien based the sound and some of the grammar of his Noldorin/Sindarin on Welsh, and Sindarin displays of the consonant mutations that characterise the Celtic (especially Brythonic) languages. The language was also probably influenced to an extent by the Germanic languages, as Tolkien was a scholar of both Old English and Old Norse.
The written script alphabet of the Elven languages is typically Tengwar, although Cirth can also be used.