
sodann
then
A formal adverb that expresses a sequence in time and means 'after that' or 'subsequently'.
Zuerst wurde der Bericht verlesen, sodann begann die Diskussion.
First the report was read aloud; then the discussion began.
then / in that case
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then
A formal adverb that expresses a sequence in time and means 'after that' or 'subsequently'.
Zuerst wurde der Bericht verlesen, sodann begann die Diskussion.
First the report was read aloud; then the discussion began.

in that case
A very formal or legal adverb that introduces a condition or consequence and means 'in this case' or 'if that is so'.
Sollte der Zeuge nicht erscheinen, sodann muss das Gericht die Verhandlung vertagen.
Should the witness fail to appear, in that case the court must postpone the hearing.
'Sodann' (then / in that case) is a very formal word. It is used almost exclusively in written language, official speeches, or legal texts.
Der Angeklagte bekannte sich schuldig, sodann verkündete der Richter das Urteil.
The defendant pleaded guilty; then the judge announced the verdict.
When 'sodann' (then / in that case) stands at the beginning of a main clause (position 1), the conjugated verb follows directly after it in position 2. This word order is called inversion.
Der Redner beendete seine Rede. Sodann klatschten die Zuhörer.
The speaker finished his speech. Then the listeners applauded.
You can often recognize the conditional meaning ('in this case') from the fact that the preceding sentence formulates a condition. Sometimes it is preceded by a conditional clause beginning with 'wenn' (if) or 'sollte' (should).
Wenn die Zahlung nicht bis morgen eingeht, sodann werden wir rechtliche Schritte einleiten.
If the payment is not received by tomorrow, in that case we will take legal action.
then
„Dann“ and „sodann“ can express the next step in a sequence of events. „Sodann“ sounds considerably more formal or elevated, while „dann“ is usual in everyday speech and storytelling. Use „dann“ in everyday situations and „sodann“ mainly in formal texts.

Wir unterschreiben den Vertrag und gehen sodann nach Hause.
We'll sign the contract and subsequently go home.
Wir unterschreiben den Vertrag und gehen dann nach Hause.
We'll sign the contract and then go home.