The verbs erinnern and sich erinnern both mean "to remember." However, they are not interchangeable and are not the only verbs used to describe the act of remembering.

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Generally, the verb erinnern means to remind someone else, while the reflexive verb sich erinnern means to remember or recall something oneself. The preposition for both verbs is an, which is followed by the accusative.

Das Geräusch erinnert an das Summen einer Biene.

The sound is reminiscent of the buzz of a bee.

Caption 26, Deutsch mit Eylin: s, ß und ss

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Er erinnerte sie daran, dass man halten muss, was man verspricht.

He reminded her that you must keep what you have promised.

Caption 66, Märchen - Sagenhaft:Der Froschkönig

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Oh, ja, das stimmt. Ich erinnere mich an die Fotos, die du mir geschickt hast.

Oh yes, that's right. I remember the photos that you sent me.

Caption 21, Die Wohngemeinschaft: Besuch

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Other verbs can imply remembering as well. The phrase an etwas denken literally means "to think of," but can be used when you want to make sure that someone doesn't forget to do something, or be applied to past events: 

Denkt an die Tage, die hinter uns liegen.

Think of the days that lie behind us.

Caption 4, Andreas Bourani Auf uns

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The verb merken can be translated as "to notice" but also "to remember." 

So merkt man sich vieles noch viel besser.

That way, you'll remember many things much better.

Caption 57, Deutsch mit Eylin: Auf natürliche Weise Sprachen lernen mit Yabla

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An important distinction should be made between the nouns die Erinnerung and das Gedächtnis. While die Erinnerung refers to an individual memory or the act of remembering, das Gedächtnis is our general capacity to store information.

Peter Barsch geht es vor allem um die Erinnerung an eine Zeit, die man heute kaum noch verstehen kann.

What matters for Peter Barsch is, above all, the remembrance of a time that you can barely understand anymore today.

Captions 26-27, 25 Jahre Mauerfall: Radtour durch die Geschichte

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Jede Zeile von mir bleibt in deinem Gedächtnis.

Every line of mine will stay in your memory.

Caption 34, Nina Chuba: Wildberry Lillet Remix feat. Juju

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Further Learning
You'll find these nouns and verbs in many examples on Yabla German.