dennoch
nevertheless
Expresses a contrast or limitation to something previously said; still, nonetheless.
Die Aufgabe war sehr schwierig, dennoch hat er sie erfolgreich gelöst.
The task was very difficult; nevertheless, he solved it successfully.

nevertheless
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nevertheless
Expresses a contrast or limitation to something previously said; still, nonetheless.
Die Aufgabe war sehr schwierig, dennoch hat er sie erfolgreich gelöst.
The task was very difficult; nevertheless, he solved it successfully.

When 'dennoch' (nevertheless) stands at the beginning of a sentence, the conjugated verb follows directly in second position. The adverb can also stand after the verb and the subject to emphasize the contrast less strongly.
Es war schon sehr spät. Dennoch las sie das Buch zu Ende.
It was already very late. Nevertheless, she read the book to the end.
'Dennoch' (nevertheless) is mainly used in written language and in more formal contexts. It expresses a clear, often argumentative contrast.
Die Statistiken zeigen einen Rückgang, dennoch bleibt die Lage angespannt.
The statistics show a decline; nevertheless, the situation remains tense.
The word is made up of 'den' and 'noch'. You can think of it as 'and even then still' or 'still despite that', which emphasizes its contrasting meaning.
Er hatte wenig Zeit, dennoch half er seinem Freund beim Umzug.
He had little time; nevertheless, he helped his friend move.
but
'aber' and 'dennoch' can both express a contrast to something said before. 'aber' is the simple and very common connecting word for a contrast. 'dennoch' means something similar to 'trotzdem' (nevertheless / still): there was a reason against it, but something happens anyway. 'dennoch' sounds somewhat more formal or written than 'aber'. Learners confuse the words because both show a contradiction. In everyday language, 'aber' is often the natural choice. 'dennoch' fits especially well when you want to emphasize that something applies or happens despite an obstacle.

Vor dem Termin war ich nervös, dennoch habe ich ruhig gesprochen.
Before the appointment I was nervous; nevertheless, I spoke calmly.
Wir haben genug Brot gekauft, aber die Milch fehlt noch.
We bought enough bread, but we still need milk.