The genitive is a case which is used to indicate whose something is.

m	des	+ s or es added to noun
f	der
n	des	+ s or es added to noun
p	der

Names add s (no apostrophe) in the genitive but names already ending in s do add an apostrophe.

Most adjectives add en

PREPOSITIONS that take the genitive:

während	during
trotz	in spite of
(an)statt	instead of
wegen	because of
innerhalb	inside

Many Germans use 'von' with the dative instead of the genitive:
Der Korb von dem Hund.
Der Korb des Hundes.

Can also use gehören (to belong to):
Es gehört Tanja.

to whom? wem?