Prepositions
Words describing relationships in space, time, and logic
A German preposition does not just add meaning — it also decides which case the noun after it takes. There are three groups, and knowing which group a preposition belongs to is most of the work. ALWAYS DATIVE: mit, nach, bei, seit, von, zu, aus (plus außer, gegenüber). ALWAYS ACCUSATIVE: für, um, durch, gegen, ohne, bis. TWO-WAY: in, an, auf, über, unter, vor, hinter, neben, zwischen. These take dative for a LOCATION (wo? — where something is) and accusative for a DIRECTION (wohin? — where something is going). The two-way test is simple: is anything moving from one place to another? If yes, accusative. If it is just sitting somewhere, dative.
In Persian a preposition never changes the word after it — «با ماشین», «در خانه», «به مدرسه» all leave the noun untouched. In German the preposition reaches into the noun phrase and rewrites the article: mit DEM Auto, in DER Stadt. So do not memorise prepositions as single words. Memorise them as a pair — «mit + Dativ» — the way you would learn a phrasal verb.