The Ancient Greeks' contributions to Western Civilization are so numerous that we can only really talk about a very few of them here.,
In mathematics, the Greeks contriubted to us the work of people like Eucild and Archimedes and Pythagoras in geometry and other forms of math. In the area of social sciences, Herodotus is known as the father of history as an academic discipline because he introduced the idea of a rational study of history (as opposed to a more mythological approach). Thucydides carried his work farther and is one of the most important historians ever. Ancient Athens, of course, is generally seen as the birthplace of democracy. We still look back to Plato and Aristotle as important thinkers on ethics and social issues.
All of these, and many more, are contributions to Western Civilization that have come from the Ancient Greeks.