Prepositions are words which define the relation between different items. Prepositions give information about direction, position and time in a sentence.
What complicates German is that prepositions usually require a certain case. In German prepositions can be divided into different groups, prepositions + Accusative case and prepositions + Dative case.
Preposition followed by the Accusative case
Preposition followed by the Dative case
Preposition followed by the Genitive case
Note:
There is a group of german preposition which take either the accusative or the dative depending on whether the emphasis is on movement or position.

You use the accusative form for direction and movement and answers the question where to. The dative form indicates position and location and answers the question where.
Examples:
English: I put the book on the table.
Preposition: on -> auf (accusative or dative form possible)
Form: accusative form -> put on the table (movement)
German: Ich lege das Buch auf den Tisch
English: The book is on the table.
Preposition: on -> auf (accusative or dative form possible)
Form: dative form -> is on the table (position)
German: Das Buch liegt auf dem Tisch
English: He is travelling by car.
Preposition: by -> mit
Form: dative form
German: Er fährt mit dem Auto
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