
augenblicklich
immediately
Without any delay; right away or at once.
Als der Feueralarm losging, verließen alle augenblicklich das Gebäude.
When the fire alarm went off, everyone left the building immediately.
immediately / currently
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immediately
Without any delay; right away or at once.
Als der Feueralarm losging, verließen alle augenblicklich das Gebäude.
When the fire alarm went off, everyone left the building immediately.

currently
At the present time; presently or at the moment.
Augenblicklich sind leider alle unsere Mitarbeiter im Gespräch.
Unfortunately, all of our employees are currently on calls.
The word derives from 'der Augenblick' (the moment), which means 'moment'. Literally, it means something like 'happening in a moment' or 'applying for the moment'.
Ein Augenblick der Unaufmerksamkeit kann zu Fehlern führen.
A moment of inattention can lead to mistakes.
As an adverb, 'augenblicklich' can stand at the beginning of the sentence (position 1) or inside the sentence. If it is in position 1, the verb follows in position 2 (inversion).
Augenblicklich habe ich leider keine Zeit für dich.
Unfortunately, I currently don't have time for you.
The meaning 'sofort' (immediately) usually describes a quick reaction to an event. The meaning 'momentan' (currently) describes a current state that does not have to be permanent. The sentence context and tense help distinguish between them.
Nach dem Anruf fuhr er augenblicklich los. (sofort)
After the call, he left immediately. (right away)
'Augenblicklich' can sound somewhat more formal or elevated. In everyday language, other words are often used for the two meanings.
Der Minister trat augenblicklich von seinem Amt zurück.
The minister resigned from his office immediately.
immediate / same
Gleich and augenblicklich can announce that an action will take place without a long wait. Gleich can also mean that it will only begin shortly, whereas augenblicklich places greater emphasis on carrying it out immediately. Use augenblicklich when any delay at all must be ruled out.

Die Ärztin behandelt den Notfall augenblicklich, weil jede Verzögerung gefährlich sein kann.
The doctor will treat the emergency immediately because any delay could be dangerous.
Die Ärztin behandelt den Notfall gleich, sobald sie mit dem Patienten nebenan fertig ist.
The doctor will treat the emergency as soon as she has finished with the patient next door.