Essential values of the genitive

[determiner/determinee?]

The genitive indicates that a relationship exists between two words, usually nouns, or the “determiner” and the “determinee.” In the end, the determinee is most often a noun (including a pronoun), but may also be an adjective or even a verb.

The genitive expresses, among other things, ...

possession:
animos Romanorum (the spirits of the Romans)
liber Petri (Peter's book)
 
quality:
uir magnæ prudentiæ (a man of great wisdom)
puer egregiæ indolis (an unexcelled child)
is magnæ prudentiæ erat (this one was of great wisdom)
 
one of a collection or a whole, related to the partitive in French:
Sabinorum quietissimus (the most peace-loving among the Sabines)
 
diverses relations after certain adjectives or verbs more or less learned on a per-word basis:
auidos belli (eager to wage war)
peritus belli (adept at waging war)
beneficiorum memini (I remember the good times)

If the accusative case in Latin has a more obvious and direct relationship with the verb and its object, the relationship of the genitive is, of course, more vague and indirect. Consequently, there exist two sorts of genitives within one ambiguous expression as illustrated by the phrase amor matris.

In the case where amor designates an emotion that a woman has for her child is termed subjective genitive whereas when amor is what I feel for my mother, it is an objective genitive.