
die Aufmerksamkeit
attention
The state in which you concentrate your thoughts and senses on a specific person, thing, or activity.
Der Lehrer bat um die volle Aufmerksamkeit der Schüler.
The teacher asked for the students' full attention.
attention
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attention
The state in which you concentrate your thoughts and senses on a specific person, thing, or activity.
Der Lehrer bat um die volle Aufmerksamkeit der Schüler.
The teacher asked for the students' full attention.

small gesture
A small gesture or small gift that serves as a sign of affection, appreciation, or politeness.
Vielen Dank für die nette Aufmerksamkeit zu meinem Geburtstag.
Thank you very much for the kind gesture for my birthday.
'Aufmerksamkeit' (attention) is derived from the adjective 'aufmerksam' (attentive). The stem 'merk' is also found in the verb 'merken' (to notice, to remember). So Aufmerksamkeit is the state in which you actively notice something.
Er hat eine hohe Aufmerksamkeit für Details.
He has great attention to detail.
For the meaning 'Konzentration' (concentration), Aufmerksamkeit is often combined with certain verbs. You can 'Aufmerksamkeit schenken' (pay attention), 'Aufmerksamkeit erregen' (attract attention), or 'die Aufmerksamkeit auf etwas lenken' (direct attention to something).
Der laute Knall erregte die Aufmerksamkeit aller Anwesenden.
The loud bang attracted the attention of everyone present.
A common construction is 'die Aufmerksamkeit auf etwas lenken' or 'richten' (to direct attention to something). The target of the attention is always in the accusative.
Ich möchte Ihre Aufmerksamkeit auf das Problem lenken.
I would like to draw your attention to the problem.
You can often recognize the meaning 'kleines Geschenk' (small gift) from adjectives like 'klein' (small) or 'nett' (nice/kind). In this case, Aufmerksamkeit is something concrete that is given as a sign of appreciation.
Als kleine Aufmerksamkeit brachte er seiner Gastgeberin eine Flasche Wein mit.
As a small gesture, he brought his hostess a bottle of wine.
interest
Interesse and Aufmerksamkeit can both be directed toward a Vortrag. Interesse refers to intellectual curiosity about or engagement with the topic; Aufmerksamkeit is the current concentration of one’s thoughts and senses. An interesting topic arouses Interesse, while a difficult explanation requires Aufmerksamkeit.

Während einer schwierigen Erklärung richten die Zuhörer ihre volle Aufmerksamkeit auf den Vortrag.
During a difficult explanation, the audience directs its full attention to the talk.
Die Zuhörer zeigen großes Interesse am Thema des Vortrags und stellen viele Fragen.
The audience shows great interest in the topic of the talk and asks many questions.