There are two German nouns that are translated as "silence"—die Stille and das Schweigen. 

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The main difference is that das Schweigen implies a conscious choice by a person to remain silent, whereas die Stille can occur naturally without human intervention. Let's have a look: 

Vom Trubel des Narzissenfestes geht es jetzt nach Osttirol in die Stille und Einsamkeit der Bergwelt.

From the hustle and bustle of the Daffodil Festival we are now heading to East Tyrol into the silence and solitude of the mountain world.

Captions 1-2, Die letzten Paradiese: Die Schönheit der Alpen 1

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There is the related adjective still, which means "silent":

Stille Nacht, heilige Nacht

Silent night, holy night

Caption 2, Weihnachtslieder: Stille Nacht mit Gabriela, Mira und Ralph

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It's important to note that while das Schweigen is related to the commonly used verb schweigen ("to remain silent"), the verb stillen ("to breastfeed") does not relate in the same way to the noun die Stille. 

Sie haben die Pflicht zu schweigen.

You have a duty to remain silent.

Caption 26, extra 3: Sprachpolizei gegen falsches Deutsch

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Die Nacht so laut, doch in mir schweigt's.

The night so loud, but inside me it's silent.

Caption 11, Joris x Lotte: Wer wir geworden sind

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The noun die Ruhe, its related adjective ruhig, and the verbs ruhen and ausruhen refer also to a quiet, calm, restful state, though not necessarily completely silent. 

Hinter dem Schloss finde ich Orte der Ruhe und Erhabenheit.

Behind the castle I find places of tranquility and [the] sublime.

Caption 18, Architektur: Karlsruher Brunnen

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Dann verordne ich mir immer ganz viel Ruhe.

Then I always prescribe myself lots of rest.

Caption 25, Deutsch mit Eylin: Erkältungszeit

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Sei ruhig!

Be quiet!

Caption 21, Deutsch mit Eylin: Der Imperativ

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Zwei Männer ruhen sich aus, einer überwacht das Gelände

Two men will rest, one will keep guard of the site,

Caption 56, Es war einmal... der Weltraum: Die Saurier

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Finally, another adjective that also can mean "quiet" is leise. It refers to a low volume.

Oh, der ist aber leise, man hört ja gar nichts.

Oh, it's so quiet, you can't hear anything.

Caption 8, heute-show: Werden Elektroautos das Klima retten?

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Further Learning
You can find all of these words on Yabla German and watch the Piggeldy und Frederick episode on die Stille for a humorous take on the topic. 

Not too long ago, we sent out a lesson on homographs, which are words that are spelled the same and sound the same, but have different meanings. You could also say that it's when one word has various definitions. Anyway, the noun der Gang falls into this category.

One translation of der Gang is "the course," as in a course of events, or the way something happens.

Hier geht alles seinen ruhigen Gang.

Here, everything runs its quiet course.

Caption 21, Die letzten Paradiese - Die Schönheit der Alpen - Part 9

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Just as a course can also refer to part of a meal in English, Germans say der erste Gang for the first course (though probably more often die Vorspeise / "the appetizer") and der Hauptgang for the main course.

Und da kommt auch schon der nächste Gang.

And here comes the next course already.

Caption 18, Die letzten Paradiese - Die Schönheit der Alpen - Part 5

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Now it's time to shift into high gear, for which we can also use der Gang, as it is used to refer to a gear that you would shift into on a bicycle or in a car. Unlike in English, it does NOT refer to a gear in a wristwatch, which is das Zahnrad (die Zahnräder as a plural noun).

Dann legen wir den ersten Gang ein.

Then we shift into first gear.

Caption 17, Fahrschule - Wie man die Kupplung bedient

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Here you can see how der Gang is used to refer to someone's gait or the act of doing a walkthrough.

Es gibt ja viele Frauen, die...

There are many women that....

ja, ihren Gang auch ein bisschen verbessern können.

yes, can also improve their walk a little bit.

Caption 15, Auf dem Laufsteg - Modelcollege in Wiesbaden

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... deshalb schwingt bei einem Gang durch das Museum auch viel Nostalgie mit.

... therefore a tour through the museum also resonates with a lot of nostalgia.

Caption 23, Flipperautomaten - Kunstwerke für flinke Kugeln

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And then there's the very common translation of der Gang as a hallway or corridor:

Der rechte Gang und dann ganz hinten links.

The right hallway and then all the way in the back on the left.

Caption 18, Mein Weg nach Deutschland - Auf Arbeitssuche

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Further Learning
You'll find many instances of der Gang used on Yabla German, but why not also try to formulate your own sentences?

Most of you hopefully know the German verb schlafen (to sleep), but are you familiar with the verb verschlafen? It's probably one of the most common reasons for people arriving to work late:

Ich bin zu spät gekommen, weil ich verschlafen habe.
I arrived too late because I overslept.

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Wo steckt eigentlich Nicki? -Verschlafen?

Where is Nicki hiding, actually? -Overslept?

Caption 41, Großstadtrevier - Von Monstern und Mördern

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Verschlafen is also common as an adjective and adverb and has a slightly different meaning:

Das Kleinste ist erst Ende März geboren und noch sehr verschlafen.

The smallest was only born at the end of March and is still very sleepy.

Caption 30, Rhein-Main-TV - Tierbabys im Opel-Zoo

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Aber noch blinzelt die Leitkuh etwas verschlafen in die Morgensonne.

But the lead cow still blinks a bit sleepily in the morning sun.

Caption 19, Die letzten Paradiese - Die Schönheit der Alpen 1

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But the most unexpected meaning of verschlafen is in its slang use with a direct object: 

Ich bin ganz ehrlich, ich hab ihn verschlafen, weil ich einkaufen war.

I'll be totally honest: I missed it because I was shopping.

Caption 18, Die Pfefferkörner - Alles auf Anfang

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This could be alternately translated as "overlooked" or "forgot." So if you ever hear somebody say that they "overslept" something, you'll know that they are using a slang idiom that means that they overlooked it — nothing really to do with sleep!

Further Learning
See if you can guess—if you don't already know—the meanings of ausschlafen, durchschlafen, einschlafen, entschlafen, weiterschlafen, and überschlafen. Then go find some examples of these words used in a real-world context on Yabla German. All this talk about sleep is making me sleepy, so with that I wish you all a good night, ich gehe jetzt schlafen!