Which case should I use with which preposition?

All prepositions in German will be followed by a case, either Dative or Accusative. Some of these are always the same, for example, "nach" (after/according to) will always be followed by the Dative, whereas "gegen" (against) will always be followed by the Accusative. There are two lists which are good to lear by heart. These are some of the most common prepositions that you'll need, and they always take the same case.. DAT: aus, bei, mit, nach, seit, von, zu, gegenüber ACC: für, durch, gegen, bis, ohne, um, entlang For many prepositions, however, it is possible for the following noun to be in either the Dative or the Accusative, depending on the cotext of the action. "In" is a classic example of this: Ich muss heute in die Schule gehen. (I have to go to school today) Er hat seine Hausaufgaben in der Schule erledigt. (He completed his homework at school) In the first example, the verb is "to go" and the school is the place to which the subject is going, so German "in" is more like the English "into". The result of "to go" is "to school". In the second example, the school is just the location where another action has taken place, which is the doing of homework. I learned this as the "movement rule": if there is a movement from one place to another, then the preposition will take the Accusative. When the verb indicates the location of another action, then the preposition will be Dative. If you learn the two lists of prepositions, and then apply the movement rule to any prepositions which are not in those lists, then you will be able to work out the correct case.