
sich hingeben
to devote oneself
To dedicate oneself completely to an activity, feeling, or passion and become absorbed in it.
Nach einem langen Tag gab er sich ganz der Musik hin.
After a long day, he devoted himself completely to music.
to devote / hand over / sacrifice
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to devote oneself
To dedicate oneself completely to an activity, feeling, or passion and become absorbed in it.
Nach einem langen Tag gab er sich ganz der Musik hin.
After a long day, he devoted himself completely to music.

to hand over
To give or hand something to someone; to give something out of one's hand.
Widerstrebend gab er dem Polizisten seinen Führerschein hin.
Reluctantly, he handed over his driver's license to the police officer.

to give oneself
To give oneself sexually to another person; to sleep with someone. This meaning can sound outdated or literary.
In dem Roman gibt sie sich dem Helden nach langem Zögern hin.
In the novel, after long hesitation, she gives herself to the hero.

to sacrifice
To sacrifice something valuable, such as one's own life, for a higher cause.
Er war bereit, sein Leben für die Freiheit seines Landes hinzugeben.
He was prepared to sacrifice his life for the freedom of his country.
'Hingeben' (to devote/hand over/sacrifice) is a separable verb. The prefix 'hin-' stands at the end in main clauses. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er gibt sich ganz der Malerei hin.
He devotes himself completely to painting.
In the meaning 'sich widmen' (to devote oneself), the verb is reflexive, and the thing one devotes oneself to is in the dative. The structure is: sich (accusative) einer Sache (dative) hingeben.
Am Wochenende gibt sie sich ganz ihrer Leidenschaft für das Gärtnern hin.
On the weekend, she devotes herself completely to her passion for gardening.
When 'hingeben' means 'überreichen' (to hand over), it usually needs a person in the dative (to whom one gives it) and a thing in the accusative (what one gives).
Er musste dem Beamten seinen Pass hingeben.
He had to hand over his passport to the official.
In the meaning 'opfern' (to sacrifice), 'hingeben' (to sacrifice) is often used with very valuable, abstract things. Typical objects are 'sein Leben' (one's life), 'seine Jugend' (one's youth), or 'sein Vermögen' (one's fortune).
Die Heldin im Film war bereit, ihr Leben für ihre Freunde hinzugeben.
The heroine in the film was prepared to sacrifice her life for her friends.
to hand in / give off
Both verbs can refer to handing an object to someone. Abgeben has a broader meaning and also works when leaving something at a designated place. Hingeben focuses more strongly on the immediate act of giving something from one’s hand to a person.

Mara gibt dem Beamten den Umschlag direkt hin.
Mara hands the envelope directly to the official.
Mara gibt den Umschlag am Schalter ab.
Mara hands in the envelope at the counter.