How do we emphasize the urgency of a situation or immediacy of an event? How can we reassure someone that something will be taken care of right away?

The adverb gleich is used a lot and has many possible translations in this context. You might be thinking about it as an adjective meaning "same" or "alike," and we also have a lesson on that topic. But here we are looking at how it is used to define something as happening "in just a minute," "immediately," or "momentarily." 

Gut, vielen Dank. Ich mache mich gleich auf den Weg.

Good, many thanks. I'll be on my way immediately.

Caption 14, Berufsleben - Probleme mit Mitarbeitern

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Warum hab ich das nicht gleich erkannt?

Why didn't I realize that right away?

Caption 80, Die Pfefferkörner - Endspurt - Part 12

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Ja, Moment, ich habe es gleich.

Yes, one moment, I'll have it momentarily.

Caption 30, Der Merkelpilot - der kleine Mann, der es macht

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There is another way to say that something will happen "any minute now," and it's very similar to how it's said in English:

Aber der Reparaturdienst müsste jede Minute da sein.

But the repair service should be here any minute.

Caption 8, Die Pfefferkörner - Endspurt - Part 18

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Another adverb to know is sofort, which is even more urgent than gleich, and is pretty much always translated as "at once," "right away," or "immediately."

Kein Problem, Frau Schmidt. Ich werde es Ihnen sofort schicken.

No problem, Ms. Schmidt. I will send it to you immediately.

Caption 67, Berufsleben - das Vorstellungsgespräch

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Sie ist sofort abgehauen, als Frau Lenz die Sache angesprochen hat.

She immediately took off when Ms. Lenz raised the matter.

Caption 65, Die Pfefferkörner - Endspurt - Part 2

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In more formal contexts, you may hear unverzüglich ("without delay") and umgehend. 

Er muss unverzüglich Waffenstillstandsverhandlungen mit Eisenhower und Montgomery aufnehmen.

He must immediately begin armistice negotiations with Eisenhower and Montgomery.

Caption 81, Die Stunde der Offiziere - Dokudrama über den 20. Juli 1944

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Oder noch besser, komm umgehend ins Kontor.

Or better yet, come to the office immediately.

Caption 65, Die Pfefferkörner - Alles auf Anfang

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Although unmittelbar is also translated as "immediate," it is often related to space rather than time: 

Wir sind, äh, hab ich schon gesagt,

We are, uh — as I've already said —

in unmittelbarer Nähe, äh, von Saarbrücken.

in the immediate vicinity, uh, of Saarbrücken.

Captions 37-38, Nachbarn - Andrea aus Forbach

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Daher ordne ich an, dass Sie unmittelbar wieder die Ehe schließen.

Therefore I order you to remarry immediately.

Captions 34-35, Yabla Gerichtshof - Probleme des Zusammenlebens

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For urgency, there is the word dringend, which like many German words functions as both an adjective and an adverb depending on how it's integrated in the sentence: 
 

Ich brauche dich hier dringend im Innendienst.

I need you urgently here in the office.

Caption 63, Großstadtrevier - Von Monstern und Mördern

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Further Learning
You will find many examples of these words used on Yabla German. In particular, keep an eye on how the translation of gleich changes depending on the context. 

Let's continue on from the first lesson about different insect names in German, starting with the sometimes rather annoying fly: 

In dem Moment ist mir eine Fliege ins Ohr geflogen.

At that moment, a fly flew into my ear.

Caption 57, 48 h in Innsbruck - Sehenswürdigkeiten & Tipps

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There are also a number of German idioms and slang usages that use the noun die Fliege:

Damit schlägt sie zwei Fliegen mit einer Klappe.

With that she hits two flies with one swatter.

Caption 7, Christina Stürmer - ist reif fürs Museum

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Hau ab! Mach die Fliege, sonst gibt's Ärger.

Get lost! Do the fly, or there'll be trouble.

Caption 39, Die Pfefferkörner - Endspurt

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The two translations above are literal, of course. Zwei fliegen mit einer Klappe schlagen has the English equivalent "to kill two birds with one stone." And die Fliege machen means to get away quickly, just as flies do. The common housefly is called die Stubenfliege, by the way.

Another potentially annoying insect is die Motte:

Kleine braune Motten mit scharfen Zähnen flogen aus der Büchse.

Little brown moths with sharp teeth flew out of the box.

Caption 54, Märchen - Sagenhaft - Die Büchse der Pandora

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Die Motten flogen aus dem Fenster und stachen jeden, der ihnen in die Quere kam.

The moths flew out the window and stung everyone who crossed their path.

Captions 63-64, Märchen - Sagenhaft - Die Büchse der Pandora

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Fliegen Motten in das Licht, genau wie du und ich.

Moths fly into the light, just like you and I.

Caption 2, Nena - Irgendwie, irgendwo, irgendwann

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Even though they're technically arachnids, not insects, let's include die Spinne: 

Alligatoren, Schlangen, Spinnen, Skorpione.

Alligators, snakes, spiders, scorpions.

Caption 3, Summer Cheergirl - Fotoshooting mit lebendigen Spinnen

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And then there are the amazing traps that spiders lay and live upon:

Das sieht aus wie ein Spinnennetz.

That looks like a spider web.

Caption 55, Die Pfefferkörner - Alles auf Anfang

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As well as an idiomatic expression that means "how horrible":

Aber einem Menschen seine Krankheit vorzuwerfen: Pfui Spinne!

But criticizing a person for his illness: ugh, spider!

Caption 54, heute-show - Die männliche Merkel hat Erinnerungslücken

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And here's another idiomatic expression using die Laus (plural: die Läuse), which is asking here if you are upset about something:

Ist Ihnen schon wieder eine Laus über die Leber gelaufen?

Did a louse walk over your liver again?

Caption 13, Weihnachtsmann gesucht - Der echte Weihnachtsmann

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Further Learning
See if you can guess the meanings of the following German insect words, and then make them plural in German and check if you were correct: die Mücke (or die Stechmücke); die Kakerlake; die Libelle; and lastly an easy one: der Grashüpfer. Then go to German Yabla and watch some other videos about insects.