What are the three types of architecture that the Romans used?

The Romans did not have three types of architecture. They adopted the three Greek orders (styles) form making columns and their capitals. They also developed the composite order, which mixed elements of two of the three main orders.

Roman architecture went way beyond just adopting the three Greek orders for columns. Its biggest feature was what historians call the Roman architectural revolution or concrete revolution. This involved the extensive use of concrete, the barrel arch and the vaulted arch.

Although the Romans were not the first in history to use concrete, they developed a type of concrete (opus caementicium) which was as resistant as modern concrete and which also set underwater (and therefore could be used to build docks for ports, dams, aqueducts and bridges). It was less fluid than modern concrete and had to be layered by hand. It was made by mixing a volcanic rock called pozzolana (which is named after Pozzuoli, a suburb of Naples) with lime and adding rubble from stones, bricks or pottery shreds as aggregates which added body to it. Concrete had technical and practical advantages. It was exceptionally strong and could span great distances when shaped into arches, vaults and domes as it could be moulded. It was layered into a formwork and it took the shape of its container. It did not require skilled labour and therefore was cheaper. It was much faster for construction than laborious masonry walls. It was safer because concrete-vaulted roofing was fireproof, unlike the wooden-beamed roofs of traditional construction methods.

With this revolution the potential of the previously little used arch, vault, and dome was fully exploited for the first time. The Etruscans are said to have invented the simple (barrel) arch. The oldest example of the vaulted arch has been found in the Greek city of Pergamon (in western Turkey). The vaulted arch came into two forms: the groin arch was formed with two to four intersecting barrel arches and the rib arch, where the intersecting barrels were not of the same diameter. The Romans were first to fully appreciate the advantages of the arch and the vault. The arch has a strong load- bearing capacity. The vault has an even greater load bearing capacity and its structure is suited to support large roofs. Their construction in concrete made them easier to build and even stronger. This led to the use larger and monumental arches and vaults on a grand scale. However, the Romans did not abandon masonry arches and vaults.

Concrete and the arch and the vault were the three elements which enabled the Romans to go beyond the use of Greek methods of enclosing space by the use of cut-stone and post-and-beam or post-and-lintel structures. They became essential for large buildings and roofs. They were used to build large buildings, such as basilicas (public buildings) amphitheatres (arenas), theatres, baths, circuses (racing tracks) domes, forts and fortifications, bridges, aqueducts, and dams. They also made it possible to build bridges which were much longer than before and could cross much wider rivers and valleys.

Concrete was also used to assist the construction of the stone-paved roads. A ditch was ploughed down to the firmest layer of ground that was found. The ditch was filled with rubble from local materials or sand (when it could be found) up to one metre from the surface level. A flat floor of compacted gravel was made. Then a surface was made by embedding the stones in concrete to create the paving. The concrete was laid in two thin layers. The bottom one had coarse concrete and the top one had fine concrete.