Final answer:
The Greeks began establishing overseas colonies due to overpopulation and a shortage of arable land, leading to emigration in search of fertile territories conducive to agriculture and trade.
Step-by-step explanation:
The primary problem that encouraged the Greeks to undertake colonization was the issue of overpopulation and the lack of arable farmland available in Greece. With increasing population levels after the end of the Dark Age, the Greeks began to face a food production crisis. The rocky and mountainous terrain of the Greek mainland was unable to support the growing number of citizens, leading to emigration in search of new lands that could provide sufficient resources.
The Greeks established colonies across the Mediterranean as far as Spain in the west and the Black Sea in the north, including significant settlements in Sicily and along the North African coast. These colonies were integral to Greek trade, exporting products such as olive oil and wine and importing grain, tin, and timber. Greek colonial ventures were often situated by the sea for easier access to trade routes and maritime commerce.
Furthermore, the establishment of these colonies led to the spread of Greek culture and the development of independent city-states, or polis, embodying Greek political institutions and societal structures. The new colonies often practiced equal land distribution among free adult males, reinforcing the concept of citizenship with equality and state governance.