Learn German: Kommst du mit mir? - Are you coming with me?

The word mit (with) is a preposition that always forces the following noun or pronoun into the Dative case. The Dative form of ich (I) is mir (me). Even though we just say "me" in English, German strictly requires this Dative form after mit.

Why does the verb Kommst come at the very beginning of the sentence?

Because this is a yes/no question! To turn a standard statement like Du kommst mit mir (You are coming with me) into a question, you simply swap the subject and the verb by moving the verb to the first position.

Wait, shouldn't there be a word for "are" in "Are you coming"?

Nope! German doesn't have an "-ing" tense (present continuous) like English does. A single verb form covers both concepts. So, Kommst du? translates perfectly to both "Do you come?" and "Are you coming?" depending on the context.