
abtauchen
to dive
To go below the surface of the water, for example when swimming or diving.
Der Taucher bereitete seine Ausrüstung vor, um gleich abzutauchen.
The diver prepared his equipment to dive down in a moment.
to dive / disappear
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to dive
To go below the surface of the water, for example when swimming or diving.
Der Taucher bereitete seine Ausrüstung vor, um gleich abzutauchen.
The diver prepared his equipment to dive down in a moment.

to disappear
Colloquial for temporarily disappearing from social or public life, often in order to have peace and quiet or to be unreachable.
Nach dem anstrengenden Projekt ist er erst mal für ein paar Wochen abgetaucht.
After the exhausting project, he disappeared for a few weeks at first.
'Abtauchen' (to dive / disappear) is a separable verb. The prefix 'ab-' separates from the verb 'tauchen' in a main clause and comes at the end of the sentence.
Er taucht für einen Moment unter der Wasseroberfläche ab.
He dives below the surface of the water for a moment.
The perfect tense of 'abtauchen' (to dive / disappear) is always formed with the auxiliary verb 'sein' because it describes a movement or a change of state.
Der Wal ist tief ins Meer abgetaucht.
The whale dived deep into the sea.
The meaning depends heavily on the context. If it is about water (lake, sea, swimming pool), the literal meaning is intended. If it is about social contacts, work, or public life, the figurative meaning 'verschwinden' (to disappear) is intended.
Sie tauchte im See ab, um sich abzukühlen.
She dived down in the lake to cool off.
The figurative meaning 'to temporarily disappear' is colloquial. It often describes the wish to take a break from stress and social obligations.
Nach der Prüfungswoche bin ich erst mal für ein paar Tage abgetaucht.
After exam week, I disappeared for a few days at first.
to dive / dip
Tauchen refers to the activity underwater as a whole and can also include staying there for a longer time. Abtauchen, on the other hand, emphasizes the transition from the surface to underwater. Use tauchen for the entire activity and abtauchen for the beginning of the movement into the depths.

Nach dem Signal taucht Lara von der Oberfläche in den See ab.
After the signal, Lara dives from the surface into the lake.
Nach dem Kurs taucht Lara eine halbe Stunde im See.
After the class, Lara dives in the lake for half an hour.