Which system was prevalent in Europe from the 9th to 15th centuries, based on relationships between lords and vassals?

The prevalent system in Europe from the 9th to 15th centuries, centered around relationships between lords and vassals, is known as feudalism. This system was characterized by a hierarchical structure where the king granted land to nobles (lords) in exchange for military service and loyalty. The lords, in turn, granted portions of their land to vassals, who would serve them in a similar manner, creating a network of obligations and protections.

Feudalism was significant because it defined the socio-economic and political structure of medieval Europe. It facilitated a system of land ownership and duty: vassals would take an oath of fealty to their lords, ensuring loyalty and service, which was integral to the stability of society during a time when centralized authority was often weak.

In contrast, monarchy represents a system of government headed by a king or queen, which was often present during the feudal era but does not specifically denote the relationships of landholding. Capitalism and socialism, on the other hand, are economic systems that emerged much later and focus on different aspects of ownership and production, thus being out of context for the question regarding medieval European systems.