What is the 'genitive case'?

The genitive case is one of the 4 german cases, the others being nominative, accusative and dative.

The genitive case is used to show possession - similar to using an " 's " in English, such as 'The man's car.'

The genitve uses different forms of 'der,' 'die,' 'das' and the plural 'die'. These are 'des,' 'der,' 'des,' and 'der' respectively.

For example: 'Das ist das Auto des Lehrers'. (Der Lehrer) - That is the car of the teacher.

Notice how the der changes to des. With masculine and neuter nouns in the genitive case, we also add an -s to the end of the noun. This is not the case for feminine or plural. For example:

'Das ist das Buch der Autorin' - (Die Autorin) - That is the book of the (female) author. 

In some instances, we need to add -es on to the end of nouns that are masculine or neuter. This is the case when the noun is short (1 syllable) and ends in a consonant. 

For example:' Der Hund des Mannes' - The man's dog.

The genitive is not commonly used in spoken German and is often reserved for more formal written pieces. It is often reworded so taht the dative case is used instead. 

For example: 'Das ist der Hund von dem Mann.'

Using the geneitive in your written work is highly stylistic and can make your piece seem much more fluent and proper. There are many other elements to using the genitive case, such as posing questions, using it in relative clauses and there are some prepositional cases which take the genitive. I would love to take the time to explain these with you thorougly and properly to help you improve your writing skills.