(from the Pantheon in Rome)
By 400 BC, the Greeks had added a third type of column to the old Doric and Ionic styles. This was called the Corinthian column, after the city of Corinth. The Greeks never actually used the Corinthian column that much, but the Romans used it a lot.
The Corinthian style is fancier and heavier than the Ionic style. In Corinthian temples, the columns have a fancier base to stand on. At the top of the columns, on the capital, there's a stone carving of acanthus leaves, under the architrave (ARR-kuh-trayv). On the architrave, as in Ionic temples, there is a continuous frieze where the triglyphs and metopes would be on a Doric temple.
To find out more about Greek architectural orders, check out these books on Amazon or in your library:
Ancient Greek Architects at Work, by J. J. Coulton (1982). An interesting look at how Greek architects worked.
Greek Architecture, by A. W. Lawrence, R. A. Tomlinson (5th edition 1996). Might be a bit out of date.