Mount Kazbek is located in northern Georgia -- the country, not the state -- in Greater Caucasus and is 5,042m high (16,541ft). This mountain is an extinct volcano, which rises above the Daryal gorge and the Georgian Military Road. The glaciers located on this mountain provide the source for the Terek River.

The mountain was first climbed by a group under Douglas Freshwill in 1868. There is a beautiful monastery at the foot of the volcano. The mountain is a tourist attraction for Georgia as many places provide three-day trips from the captial of Georgia, Tbilisi, to the mountain and back. It is the second most popular peak of the Caucasus, the first is Elbruz, and is climbed by 100-150 people each year. 1

There are a lot of sites dedicated to this mountain and trips, which is where I recieved the above information. They all have almost the same info on them.
