Valyrian

Valyrian is actually a family of languages, stemming from High Valyrian, a language spoken in the ancient Valyrian Freehold. As they conquered various cities on the Continent of Essos, they would require the people there to at least speak a little High Valyrian. After the doom of Valyria, about 400 years before the time of the War of the Five Kings (the time of the books), High Valyrian ceased to be widely spoken. it became a dead language, much like our Latin is a dead language today. Although spoken by a few families, scholars, and priests, it is not in common use.

Instead, High Valyrian was assimilated into the local languages of the people who were once under the subjugation of the Freehold of Valyria. The result was a wide range of ‘bastard Valyrian’ languages which were more or less incomprehensible from town to town. In the area of Astapor, High Valyrian mixed with the old Ghiscari language, plus the local language to create Astapori Valyrian, another language featured in this site. Although the High Valyrian influence can cleary be seen in Astapori Valyrian, it is very much a different language.

You can learn Valyrian here http://wiki.dothraki.org/Learning_High_Valyrian