What are some of the contributions that Ancient Greece and Rome gave?

Ancient Greece and Rome provided the foundation for all of the ideas that modern western societies use to understand themselves. In the case of Greece, all of the sciences find their origins in Greece itself or during the Hellenic period following the conquests of Alexander the Great. Politically, democracies and certainly western democracies are thought to originate from ancient Greece. Also, Roman law defines both literally (since legal language is frequently Latinate) and figuratively the way modern legals systems operate. Culturally, the first theatre performances and hence, the most fundamental dramatic conventions were developed in ancient Greece along with the first literature with the writing down of the Iliad and the Odyssey. Perhaps the most obvious contribution to western languages is Latin of which French, Italian, Spanish, Portuguese and Romanian are its children. English also uses a great deal of latinate words, particularly in scholarly or scientific language. Essentially, anything you can think of today, it is possible to trace its origins back to antiquity in a way that will always surprise you.