You may know one or both of the words in the title above: der Mut means "the courage" and mutig means "courageous" or "brave." However, there are many nouns, verbs, adjectives, and adverbs that contain these words as roots, some of which have nothing to do with courage. Let's have a look.

As you can see, nouns ending in -mut may refer to a mood, emotional state, or feeling:

Hochmut kommt vor dem Fall.

Pride comes before the fall. 

Caption 24, Eva erklärt - Sprichwörter

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Was bei vielen Autofahrern für Freude sorgt,

What causes happiness among many drivers,

stiftet Unmut bei den Grünen.

causes discontent among the Greens [Green Party].

Caption 19, Deutsche Autobahnen - Geschwindigkeitsbegrenzungen

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Die Queen residierte hier bereits und Michael Jackson

The Queen resided here already and Michael Jackson

hielt im Übermut sein Baby aus einem Hotelfenster.

held his baby boisterously out of a hotel window.

Captions 24-25, Berlin - Hotel Adlon feiert 15 Jahre Neueröffnung

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...in spektakulärer Anmut auf die Wasseroberfläche zu klatschen.

...to smack against the surface of the water with spectacular grace.

Caption 8, Evolution - Meeresbewohner

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Notice above that der Hochmut, der Übermut, and der Unmut are masculine, while die Anmut is feminine. You can also look up der Wagemut, der Missmut, die Sanftmut, and die Schwermut. For der Demut, you may more often see the related adjective (note the umlaut!):

Es war jedenfalls demütigend genug.

In any case, it was humiliating enough.

Caption 20, Lerchenberg - Das Wunder

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It's additionally good to know the adjectives ermutigend and entmutigend. These respectively mean "encouraging" and "discouraging."

When it comes to verbs, you may have seen zumuten, vermuten, and anmuten. These verbs each have a number of possible meanings.

Man vermutet, hier ist irgendwas in der Lüftung vom Willy-Brandt-Haus.

One suspects there is something in the ventilation here in the Willy-Brandt-Haus.

Caption 75, heute-show - Die männliche Merkel hat Erinnerungslücken

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Traditionen sind was Schönes

Traditions are something nice

und können für Nichteingeweihte mitunter ganz schön skurril anmuten.

and can occasionally appear quite bizarre to the outsider.

Captions 1-2, Barfuß unter Schafen - Schäferwettrennen

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Petrus muss Dortmund-Fan sein, anders ist kaum zu erklären,

Saint Peter must be a Dortmund fan, there's almost no other explanation

was der Himmel dem FC Bayern und seinen Fans zugemutet hat.

for what the heavens had in store for FC Bayern and its fans.

Captions 1-2, FC Bayern München - Triple-Feier im Dauerregen

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Further Learning
Look up these words using your favorite online dictionary or on Yabla German to understand the full extent of their meanings. Keep in mind that there are other nouns ending in -mut that are unrelated to emotional states, such as das Mammut or der Wermut.

After some very pleasant summer weather, the last week has been very rainy in Germany. Like English, German has many words and expressions to describe different types of rain. Let's take a look at some examples from Yabla German. 

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In Berlin, we most often only have vereinzelte Schauer (what we refer to in English as "scattered showers"), but in other parts of the country flooding can become a real problem: 

Heutiger Hochwasserstand: wieder mindestens zehn Zentimeter.

Today's flood water level: at least ten centimeters again.

Caption 44, Die Klasse - Berlin '61

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Even when it isn't dangerous, rain can create a lot of complications: 

Der Dauerregen drückte zwar nicht auf die Stimmung...

The constant rain didn't dampen the mood...

Caption 7, FC Bayern München - Triple-Feier im Dauerregen

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The Piggeldy and Frederick cartoon linked below has quite an exhaustive list of types of rain: 

Es gibt Platzregen, Dauerregen, Sprühregen,

There are cloudbursts, [there is] constant rain, misty rain,

Nieselregen, Eisregen, Landregen, Gewitterregen,

drizzle, freezing rain, steady rain, thunder shower,

Sommerregen, Winterregen und Bindfadenregen."

summer rain, winter rain and string-like rain [pouring rain]."

Captions 10-12, Piggeldy und Frederick - Regen

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One other word to know is der Niederschlag ("precipitation") which is often used in weather reports:

Von Westen her kommen dann wieder Tiefausläufer,

Low-pressure areas are then coming from the west again,

die dann eben auch Niederschlag mit sich bringen können.

which can also then bring precipitation with them.

Captions 22-23, Rheinmain im Blick - Der Frühling ist da

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Further Learning
What kinds of rain are common where you live? Try to find the equivalent in German. For a challenge, watch this weather report for last week from der Spiegel.