Minoans lived on the island of Crete. The culture was centred on magnificent palaces. Its art work included frescoes with humans, fish, vegetation and animals. Bulls and snakes were important in their art and religion. Three different undeciphered scripts Linear A, Hieroglyphic A, and Hieroglyphic B were used. Minoans traded with Egypt. The were conquered ca. 1500 BC by the Mycenaeans.
Mycenaeans: This is the culture putatively described in Homeric epic. They flourished on the mainland of Greece, and were influenced by and traded with the Minoans whom they eventually conquered. They spoke Greek. They wrote Greek in a syllabary known as Linear B which was deciphered in the 1950s. The culture ended ca. 1200 BC.
Athens: The great Greek democracy of the mainland known for its art, philosophy, and drama.
Sparta: A militaristic city-state kingdom located on the Peloponnesus.
Sparta had a unique social system based on the rules of the (potentially legendary) Lycurgus. The agoge was the schooling system for Spartan boys; it taught them to work as a team with each other and other Spartan values (austerity, loyalty, obedience, patriotism) - Xenophon's Spartan Constitution is a good source of information for Spartan life, and it's fairly short (take the information with a grain of salt, however, because there is no way of knowing how accurate it is considering Xenophon was an outsider). They were also strongly religious; on multiple occasions, the Spartans actually turned away from battle because they took something such as an earthquake as a bad omen. Their political system was also quite unique: a dual kingship (one king from the Agiad family and one from the Eurypontid family), five ephors that basically had veto power over the kings, and the gerousia, which was a council of 28 men aged sixty or older and the two kings. Women also had more freedom: they were encouraged to exercise in public (often naked) in order to stay in shape, which would help them give birth to stronger babies. (One fun fact is that the only time a Spartan got a headstone was when they died in battle or childbirth.) They were wary of strangers (xenophobic) because they didn't welcome any potential change to their established system.