Before the Christian era, and as long ago as 600bc, most ancient Greek architecture and temples were built of wood and then they went through a 'petrification', which means the wood was either replaced or surrounded by stone, slowly, year by year.This happened to the ancient Greek Temple of Hera at Olympia.
Doric
Ionic
Corinthian
The Doric style is sturdy and its top is plain. This style was used in mainland Greece and the colonies in southern Italy and Sicily.
The Ionic style is thinner and more elegant. Its topl is decorated with a scroll-like design (a volute). This style was found in eastern Greece and the islands.
The Corinthian style is seldom used in the Greek world, but often seen on Roman temples. Its capital is very elaborate and decorated with acanthus leaves.
What we know of ancient Greek architecture is from the late archaic period, circa 500BC, the Periclean age (450-430BC), and early pure classical from 440 - 400BC, is from the Temples, which were the only buildings that survived in large numbers.
Since Roman architecture, copied ancient Greek architecture and the Hellenistic periods of building, according to writers such as Vitruvius, from the 1st century, indeed we are lucky that the few of the beautiful Greek Temples have survived, such as the Parthenon, and Temple of Hephaestus at Athens.
Greek / Roman Architecture
The architect was the craftsman and builder in the ancient Greek architecture period, he was not afforded the distinction that today's architects enjoy. He hired the workers, just as modern building contractor would. The ancient Greek architect, Iktinos, who designed and built the Parthenon would be classed as a genius today. In his day he was just a paid contractor.
There were two main styles (or "orders") of early Greek architecture as seen above, the Doric and the Ionic. These names were used by the Greeks themselves, they believed that the styles descended from the Dorian and Ionian Greeks of the Dark Ages, we do not know if this is certain.
The Doric style was used in mainland Greece and spread from there to the Greek colonies in Italy. The Ionic was used in the cities of Ionia, now the west coast of Turkey and some of the Aegean Islands. By this stage, the roads and bridges and stone walls began to be replaced.
By this time, The ancient Greeks were big into Democracy, and building palaces or big tombs was frowned upon, because politically, all men are supposed to be equal, therefore it would look bad to have a big palace even if you could afford it. Instead, the Greeks build public buildings: gymnasiums, and public meeting places where men can get together and talk.
The Greeks are well known for their amphitheaters
By the 300's BC, in the Hellenistic period, there are some new architectural types. Less time is spent on temples. The new form is the theatre, and many theatres are built all over the Greek world.
Also, there is new interest in town planning. 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.