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.

'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 both express an order or a consequence. 'dann' is the normal everyday word: you use it for 'after that', but also for the result of a condition. 'sodann' has a similar meaning, but sounds very formal and is more likely to appear in official texts, instructions, or legal sentences. The words can be confused because their meanings are close. In conversation, 'dann' is almost always natural. Choose 'sodann' only when the text is deliberately meant to sound factual or official.

Der Antrag wird geprüft; sodann erhält der Kunde eine schriftliche Antwort.
The application is reviewed; then the customer receives a written response.
Aylin kauft zuerst Brot und geht dann zur Apotheke.
Aylin first buys bread and then goes to the pharmacy.