Final answer:
The Archaic period in Greece saw the rise of tyrants and the birth of democracy, while the Classical period was characterized by the development of democratic institutions in Athens, contrasting with the oligarchy of Sparta. Political changes of these periods significantly shaped the future of Western political thought and governance.
Step-by-step explanation:
The political background near the end of the Archaic period and throughout the Classical period in Greece was characterized by significant changes and developments. In the Archaic period (c. 600-480 BCE), we saw the rise and fall of tyrants in various city-states including Athens, and the establishment of democracy by the statesman Kleisthenes in the years 508 and 507 BCE. This laid the groundwork for the more developed democratic institutions that emerged in the Classical period (500-323 BCE), which are particularly exemplified by Athens, where direct democracy allowed all male citizens to participate in the Assembly, the Council, and the judicial system.
Athens' political structure contrasted with other city-states like Sparta, which maintained a more oligarchic system, governed by a small group of elites. The Classical period was also marked by cultural achievements and significant warfare among city-states, which had permanent effects on the political landscapes of these ancient societies.