Depending on the location you have to build a house in the mountains, almost any type of house will work. Multi-level houses are often built to follow the contour of the mountain. The slope of the land and stability of the site can make a difference on the type of house you build.
Masonry (stone work) since water is usually at a premium and so they would generally not be making brick.
Concrete
Stilt houses are very common in Asia surprisingly this type of house is also built in the elevated ground.
Tenement houses are built in Glasgow
Stilt houses are very common in Asia surprisingly this type of house is also built in the elevated ground.
Not usually, but sometimes they do. In Tennesee and there are some beautiful houses on the sides of mountains.
pioneers built their own houses
The largest Anasazi houses, at the peak of their civilization, were built of stone, adobe bricks, and tuff. (A type of stone)
Choctaw houses were built of clay mixed with haulm [straw or grass].
In the UK, houses built in the 1980s were fairly similar to houses built in the 1970s and those built now. Very recent houses tend to be smaller.
Pilgrim workers built the houses. The houses on Plymouth Plantation were made out of logs, hay, rocks, wood and mud.
The Roman houses were built in the city of Rome and in all the towns the Roman built around the Roman Empire, especially in Italy. The Romans also built houses on their farms.