behalten
to keep
To leave something in one's own possession and not give it away, sell it, or return it.
Den Rest des Geldes können Sie als Trinkgeld behalten.
You can keep the rest of the money as a tip.

to keep
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to keep
To leave something in one's own possession and not give it away, sell it, or return it.
Den Rest des Geldes können Sie als Trinkgeld behalten.
You can keep the rest of the money as a tip.

'Behalten' (to keep) is an inseparable verb. The prefix 'be-' remains firmly attached to the verb stem 'halten' in all tenses and sentence constructions.
Er behielt das Geheimnis für sich.
He kept the secret to himself.
The verb 'behalten' (to keep) almost always requires a direct object in the accusative. You always keep 'etwas' (something).
Darf ich diesen Stift behalten?
May I keep this pen?
In the meaning 'sich erinnern' (to remember), 'behalten' is used reflexively with a dative pronoun. The structure is: 'sich (dative) etwas (accusative) behalten'.
Ich kann mir neue Vokabeln nur schwer behalten.
I have a hard time remembering new vocabulary.
To express that someone does not pass on a secret, you use the fixed expression 'etwas für sich behalten' (to keep something to oneself). The reflexive pronoun changes according to the person.
Kannst du das bitte für dich behalten?
Can you please keep that to yourself?
When 'behalten' (to keep) describes maintaining a state, it is often combined with abstract nouns. Common expressions are 'die Ruhe bewahren' (to keep calm), 'die Nerven behalten' (to keep one's nerve), or 'einen kühlen Kopf behalten' (to keep a cool head).
Obwohl alle panisch waren, hat sie die Nerven behalten.
Although everyone was panicking, she kept her nerve.
The expression 'Recht behalten' (to be proven right) means that an earlier claim or assumption has turned out to be correct. It describes the result over a longer period of time.
Ich habe es dir doch gesagt! Am Ende habe ich wieder einmal Recht behalten.
I told you so! In the end, I was proven right once again.
to forget
'vergessen' and 'behalten' are opposites when it comes to information in memory. 'vergessen' means that you no longer remember something. 'behalten' means that something stays in your head. Learners may confuse 'behalten' because it can also mean not giving something away. In this relation, however, it is about memory: you can retain a rule in your memory or forget it.

Lena behält neue Wörter besser, wenn sie sie laut wiederholt.
Lena remembers new words better when she repeats them out loud.
Ich habe den Namen des neuen Nachbarn leider vergessen.
Unfortunately, I have forgotten the name of the new neighbor.