Final answer:
Cities in Europe grew after the Dark Ages mainly due to an increase in agricultural productivity, which allowed more people to move to urban areas, stimulating trade and weakening the feudal system.
Step-by-step explanation:
The growth of cities in Europe after the Dark Ages can be primarily attributed to the increase in agricultural productivity. This enhanced productivity meant that fewer people needed to work the land, allowing others to pursue different trades in urban areas. Technological advancements and an agrarian revolution supported a surplus of crops, which enabled a greater portion of the population to move to cities. This urban migration led to an increased demand for goods and services, further contributing to urban growth. As cities became centers of trade and commerce, they kept expanding, which, in turn, facilitated the decline of feudalism. The demographic explosion resulted in the rising population of major cities, such as Venice, Florence, and Milan, which reached over 100,000 inhabitants by the 13th century. This urbanization is reflected in the substantial migration from the countryside to cities, contributing significantly to the growing economies and diversifying the social structure within these urban centers.