One confusing element in German syntax is the difference between subordinate clause conjunctions and main clause connectors. While the former send the conjugated verb to the end of a sentence, the latter are followed by the conjugated verb and the subject and thus cause an inversion of the two. So which category do nachdem/danach, bevor/vorher belong to?
Nachdem is a subordinate clause conjunction. Its translation "after doing something.." already indicates that there must be a difference in tense between the action of the subordinate clause that precedes the action of the main clause. Here are two examples showing you the tenses we normally use:
Nachdem ich mein Frühstück gegessen habe, lese ich meine E-Mails (Perfekt-present tense)
Nachdem ich mein Frühstück gegessen hatte, las ich meine E-Mails or habe ich meine E-Mails gelesen (Plusquamperfekt-Präteritum/Perfekt)
Danach does not subordinate but rather connects two main clauses stylistically. The difference in tense is not necessary here.
Ich habe (zuerst) mein Frühstück gegessen. Danach habe ich meine E-Mails gelesen.
Ich aß (zuerst) mein Frühstück. Danach las ich meine E-Mails.
The same applies to the difference between bevor and vorher. Whereas bevor is a subordinate clause conjunction, vorher is a main clause connector.
Bevor ich meine E-Mails lese, habe ich gefrühstückt.
Bevor ich meine E-Mails gelesen habe, hatte ich gefrühstückt.
Often, native speakers do not use different tenses with "bevor" though, so sentences like "Bevor ich meine E-Mails lese, frühstücke ich" have become acceptable, too.
Ich lese (gerade/jetzt) meine E-Mails. Vorher habe ich gefrühstückt.
Ich las meine E-Mails. Vorher frühstückte ich.
Watch out, though: if you only want to say ”before” or “after” followed by a noun, you have to use the two-way preposition vor or the dative preposition nach.
For other examples of subordinate clause conjunctions and main clause connectors, check out my post on word order in the German language. On my blog, you will also find articles on the Konjunktiv 2 in German, the difference between "um...zu" and "damit", on when to use "als" and "wenn", infinitive clauses with zu in German, adjective endings in German, and other topics like a review of the most popular online dictionaries dict.cc, dict.leo, Linguee and Collins, and a comparison between the language learning apps Duolingo, Memrise, Babbel, and Busuu.
