The Greeks wanted to destroy the Persian fleet to remove its threat to their cities.
The Persians wanted to destroy the Greek fleet so that the Greek cities would keep their armies at home defending their cities abainst amphibious attack, and they could then defeat the cities one by one, rather than allowing them to joint together in the field.
Battle of Salamis happened in -480.
It was a sea battle. The Greek fleet assembled at the island of Salamis in preparation to fighting the Persian fleet.
480
The Battle of Salamis took place in the strait between Piraeus and Salamis Island, an island in the Saronic Gulf near Athens.
In the strait between the island of Salamis and Athens.
In the bay between the island of Salamis and Athens.
Xerxes I of Persia was defeated in the naval battle of Salamis by Athenian admiral Themistocles .
In the strait between Salamis Island and Athens.
Approximately 1 month! :D The question you mean is : how long did the battle of salamis last? ;)
Between the Island of Salamis and the Greek mainland near Athens.
In the straits between mainland Greece and the Island of Salamis, September 480 BC. The battle was a decisive Greek victory
Salamis which destroyed Persian sea power.