What are German modal particles (ja, doch, mal, denn, wohl, eben) and how do I use them?

Modal particles are small, untranslatable words that add nuance, emotion, or attitude to a sentence. They don't affect grammatical meaning but are crucial for sounding natural.

doch: contradiction, emphasis, surprise, encouragement. Komm doch mal her! (Do come here!)

ja: obviousness, confirmation, agreement. Das ist ja toll! (That's great, as you know!)

mal: softening a request, indicating short duration. Warte mal kurz. (Wait a moment.)

denn: curiosity, softening a question. Was machst du denn hier? (What are you doing here?)

wohl: assumption, probability. Er wird wohl müde sein. (He's probably tired.)

eben/halt: resignation, "that's just how it is." Es ist eben so. (That's just the way it is.)