The dative case is used for the indirect object (that's the noun or pronoun which is impacted indirectly by the action, as opposed to the one to which the action is done directly). The classic example is he gives me the book (er gibt mir das Buch), where the direct object is the book and the indirect object is me. The dative also follows certain prepostions (words like with, to and between). All determiners (that's words like the and a) change in the dative, although a couple of personal pronouns are the same as in the accusative. The most important ones to remember are ich (I) becomes mir (me) and du (you) becomes dir (you).
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