What are the uses of the genitive case?

The genitive case is one of the most commonly used cases in the Russian language. Luckily for Russian scholars, it is fairy easy to master its usage:

1. To denote possession - книга Машы (lit. the book of Masha) -
2. To denote absence - У него нет книги (lit. he does not have a book)
3. To express the direct object of the sentence - this is a little more nuanced, it can only encompass animate male singular, and all animate plurals
4. After certain prepositions (e.g. для, из, от)