
verzichten auf
to give up
To voluntarily decide not to do, use, or claim something, even though one could or would like to.
Um gesünder zu leben, verzichte ich auf Zucker und Alkohol.
To live more healthily, I give up sugar and alcohol.
to give up / to do without
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to give up
To voluntarily decide not to do, use, or claim something, even though one could or would like to.
Um gesünder zu leben, verzichte ich auf Zucker und Alkohol.
To live more healthily, I give up sugar and alcohol.
The verb 'verzichten' is almost always used with the preposition 'auf' followed by the accusative. You cannot use a direct accusative object without 'auf'.
Ich verzichte auf den Nachtisch, ich bin schon satt.
I'll skip dessert; I'm already full.
People often give up stimulants, habits, or possessions. Typical combinations are 'auf Fleisch verzichten' (to give up meat), 'auf das Auto verzichten' (to do without the car), or 'auf Süßigkeiten verzichten' (to give up sweets).
Viele Menschen verzichten in der Fastenzeit auf Alkohol.
Many people give up alcohol during Lent.
When you give up doing something (that is, an action), you use the construction 'darauf verzichten, zu + infinitive' or 'darauf verzichten, dass ...'.
Ich verzichte darauf, ihn heute noch anzurufen.
I won't call him today after all.
to contain / abstain
„Sich enthalten“ and „verzichten“ both mean consciously choosing not to do or use something. „Sich enthalten“ sounds more formal and, in this usage, is usually followed by the genitive, whereas „verzichten“ is commonly used in everyday speech with „auf“ and the accusative. „Verzichten“ is usually the better choice for everyday statements.

Er verzichtete während des gesamten Abends auf Alkohol.
He did without alcohol throughout the entire evening.
Er enthielt sich während des gesamten Abends des Alkohols.
He abstained from alcohol throughout the entire evening.