The first great Greek civilization was that of the Mycenaeans, which lasted from c.1600 to c.1100 BC. Much of Greek mythology concerns the Mycenaean world, especially the Homeric stories of The Iliad and The Odyssey.
This world supposedly ended with the 'invasion' of the Dorians who eventually settled in the Peloponnese and southern Greek islands like Crete. This period also saw Greek colonization of some Aegean islands and the western coast of Asia Minor.
In the period following these events, which is called the Greek 'Dark Ages' (c.1100 - 800 BC) there emerged the distinctly Greek political organization called the 'polis' or 'city-state'. The city-state replaced monarchy, and each polis was distinctively different and fiercely independent.
During the period between c.750 and c.550 BC, much of the Mediterranean, Aegean, and Black Sea regions were colonized and new 'poleis' were established by emigrants from a mother-city.