The earliest buildings that were built in Greece, in the New Stone Age, are small houses or huts, and wooden walls around them for protection. Later there are bigger houses, and stone walls around the villages.
By the Early Bronze Age, we find one bigger house in the middle of the village, and fancier, bigger stone walls.
In the Late Bronze Age, under the influence of Western Asia, and the Minoans on Crete, there are palaces and big stone tombs, as well as paved roads and bridges, and dams (and more stone walls).
During the Greek Dark Ages the palaces were burned, and the roads and bridges and dams mostly fell apart. But at the end of the Dark Ages, with the beginning of the Iron Age and the Archaic period in Greece, we see a new type of building: the temple for the gods. These earliest temples are built in the Doric style. There are houses, but no more palaces. But roads and bridges and stone walls begin to be built again.
In the Classical period, there are more temples, bigger and with new design ideas: the Parthenon is built in the 440s BC. People begin to build in the Ionic style. Democracy prevents the Greeks from building palaces or big tombs, because politically all men are supposed to be equal, and so it would look bad to have a big palace even if you could afford it. Instead, the Greeks build public buildings: gymnasia, and stoas, where men can meet and talk.
By the 300s BC, in the Hellenistic period, there are some new architectural types. Less time is spent on temples. The new form is the theater, and many theaters are built all over the Greek world. Also, there is new interest in town planning at this time: streets begin to be laid out in straight lines, instead of just developing naturally. With the conquests of Alexander the Great, architecture becomes an important way to spread Greek culture and show who is in charge in the conquered countries.
On the other hand, once the Romans conquer Greece, around 200 -100 BC, they too use architecture to show that they are in charge, and suddenly there is a lot of building in the Roman style. Corinthian architecture became more popular. About 400 AD, the Greeks convert to Christianity, and begin to build churches and monasteries.
During the Middle Ages, parts of Greece were taken over by the Normans, who built castles, and other parts were still controlled by the Byzantine Empire, and built in a more West Asian style. Finally, in 1453 AD, the Byzantine Empire was taken over by the Turks, and Islamic mosques began to be built in Greece.