There were several minor fights in northern Greece, and a delaying action at Thermopylae. The main battles were the sea battle at Salamis and the land battle at Plataia.
It depends what you want to call Greece. It comprised 2,000 independent city-states stretching around the Mediterranean and Black Seas. And it depends what you call an invasion.
The Persians first put down a revolt in Asia Minor by Greek city-states within its empir 499-493 BCE. It sent a punitive expedition against Eretria and Athens for interfering in the Ionian Revolt 490 BCE. It sent an invasion to subdue the cities of mainland Greece 480-479 BCE. It fought several battles in Asia Minor and in the Islands of the eastern Mediterranean 478-449 BCE.
Marathon and Plataea.
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Now, Greece is a nation state. In ancient times, each city was it's own nation. The cities cooperated only during times of extreme crisis, such as the Persian invasions.
Greece has had many wars but this question has yet to be discovered
Mainland Greece in ancient times was not part of the Persian Empire, though many Greek lands in what is now Turkey were conquered by Persia. It was Greek military resistance to two Persian invasions that kept it out of the Persian Empire.
Persia lost.
The Greek city-states of Asia Minor were induced to rebel against Persian rule. Cities from mainland Greece intervened, inducing Persia to determine to bring them under control. Many agreed, but some resisted, and the Persians invaded to establish control over them.
Greece has been invaded many times by many peoples over ten thousand years or so. What is your starting point for the first and second invasions?
Herodotus of Halicarnassus wrote a work Histories in which contains 9 books. Books 6 to 9 cover the Persian Wars 499 to 478 BCE. (the wars went on for another 30 years).
Persia was a main one, but that's a difficult question, seeing as Greece was divided into many different City-States, and there were wars between them. Such as the Pellopenisian war between Athens and Sparta.
Persia invaded Greece simply because they were expanding. This resulted in many revolts from the Greeks (Greco-Persian Wars). Honestly you can simply Google the answers, but yeah they were expanding their empire. -I take AP World History and just went over the chapter- :)
All of the Persian Gulf wars concerned oil. The US utilizes many automobiles. The US has been involved in all or most of the Persian Gulf wars in the 20th and 21st centuries; specifically which Persian Gulf War concerns your question?