Well, Zeus is usually seen as the leader of the gods, but the big three were Zeus, Poseidon, and Hades. If you're asking if there's one "God" like in Christianity, then no, there isn't. There are lots of gods.
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They did not. Neptune was a Roman god. But the Greeks built temples to their sea god, Poseidon.
Because he was the god of wine.
Zeus, the god of the sky and thunder, was known as the king of the Greek gods.
The Romans had a pantheon of gods which they worshipped. In particular, Jupiter was the chief god, and the god of sky and thunder.
The greek worship Athena because she's the patron goddess of the city, and all people goes to the temple of Athena to worship her because if they don't the goddess will not allow them to get foods from her.