That's some mighty million-dollar question.:) Genitive is one of the most ubiquitous cases, so you see it used a lot. As a beginner, here is what you should know: 1. Genitive of negation: «У меня есть» + Nominative → «У меня нет» + Genitive 2. Partitive use and stating quantities: • a bucket of apples = ведро яблок • a cup of tea = чашка чая (чаю) → note that a few masculine nouns for substances have an alternative form (optional, and only чаю is still rather popular). • a lot of apples / few apples = много яблок / мало яблок 3. With A LOT of prepositions. Like у, из, от, с, возле, около, без... Note how often it governs prepositions that mean absence or separation (без, от, из, с, вне). So, you use Genitive here: • У мамы есть кот. • Я живу возле театра. • суп без мяса 4. As a possessive modifier and in the analogue of English noun chains, which truly help this to be the "of-case": • суп твоей бабушки = your grandmother's soup • ответ учителя = the teacher's answer • Министерство культуры = Ministry of Culture • теория относительности = the theory of relativity / relativity theory 5. With numbers (in Nominative). It depends on the last word in the phrase for the number: • 1 машина, 2 (3,4) машины, 5 машин (and when it is >5) 6. And, of course, most of the Accusative forms copy either the Nominative of the Genitive one (only feminine nouns in singular have a unique Accusative form).

The genitive is most regularly used to denote possession (most typical use). However, it does govern other uses:for instance, "the genitive of negation", where the genitive is used after «нет» -- ex. no problem -- нет проблемы. It is also used for counting (think of it as the numbers are in possession of the subject to which they tally). And haha when all else fails at comprehenion, you can also always think of the genitive as "the case that governs when I need to consider an 'of' before the word" hope that this helps! тебе удачи))