umgehend
immediately
At once, without culpable delay or unnecessary postponement. This word is often used in formal or business correspondence.
Bitte überweisen Sie den Rechnungsbetrag umgehend.
Please transfer the invoice amount immediately.

immediate
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immediately
At once, without culpable delay or unnecessary postponement. This word is often used in formal or business correspondence.
Bitte überweisen Sie den Rechnungsbetrag umgehend.
Please transfer the invoice amount immediately.

'Umgehend' (immediately) is derived from the verb 'umgehen' (to go around / deal with). The meaning 'sofort' (immediately) comes from the old idea of doing something 'ohne Umweg' (without a detour). So you do not go around a problem, but directly toward it.
Der Schaden wurde umgehend repariert.
The damage was repaired immediately.
This word belongs to formal language and is mainly used in business or official correspondence. In everyday language, one would more likely say 'sofort' (immediately) or 'gleich' (right away).
Wir bitten um eine umgehende Antwort auf diese E-Mail.
We request an immediate response to this email.
'Umgehend' (immediately) can be used as an adverb describing a verb, or as an adjective before a noun. Both uses are common in formal contexts.
Wir werden Ihre Anfrage umgehend bearbeiten.
We will process your request immediately.
immediate / same
'gleich' and 'umgehend' can both mean that something happens without a long wait. 'gleich' is the normal word in everyday language and can also sound a bit softer: you do something very soon, but not always in the same second. 'umgehend' sounds more formal and more binding. It is often used in emails, letters, at work, or in important situations. It means: without unnecessary delay. In conversation, you are more likely to say 'Ich rufe gleich an' (I'll call right away); in a message, you are more likely to say 'Bitte melden Sie sich umgehend' (Please get in touch immediately).

Nach dem Gespräch hat der Arzt den Bericht umgehend geschickt.
After the conversation, the doctor sent the report immediately.
Wir rufen gleich in der Praxis an, weil der Termin wichtig ist.
We'll call the doctor's office right away because the appointment is important.