die Anwesenheit
presence
The state of being physically present at a particular place; being there.
Der Lehrer überprüfte die Anwesenheit der Schüler zu Beginn der Stunde.
The teacher checked the students' attendance at the beginning of the lesson.

presence
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presence
The state of being physically present at a particular place; being there.
Der Lehrer überprüfte die Anwesenheit der Schüler zu Beginn der Stunde.
The teacher checked the students' attendance at the beginning of the lesson.

'Anwesenheit' (presence) is the noun related to the adjective 'anwesend' (present). Both words contain the old root 'wesen,' which means 'to be.' So 'An-wesen' literally means 'being there.'
Alle anwesenden Gäste waren von der Rede begeistert.
All the guests present were enthusiastic about the speech.
The formal phrase 'in Anwesenheit von jemandem' means 'while someone is present' and requires the dative. It is often used in official or legal contexts.
Der Vertrag wurde in Anwesenheit eines Notars unterschrieben.
The contract was signed in the presence of a notary.
In connection with people, 'Anwesenheit' (presence / attendance) is often used in fixed combinations. Examples are 'Anwesenheitspflicht' (mandatory attendance, at university), 'Anwesenheit überprüfen' (to check attendance), or doing something 'in jemandes Anwesenheit' (in someone's presence).
Für dieses Seminar besteht Anwesenheitspflicht.
Attendance is mandatory for this seminar.
In scientific or technical texts, 'Anwesenheit' (presence) describes the occurrence of a substance. Typical verbs used with it are 'nachweisen' (to detect/prove) or 'feststellen' (to determine/establish).
Im Wasser wurde die Anwesenheit von Bakterien nachgewiesen.
The presence of bacteria was detected in the water.
visit / visitor
'Besuch' and 'Anwesenheit' can both have to do with being at a place. However, 'Besuch' usually describes someone coming to a person, a place, or an event. So it often includes a sense of movement or a purpose. 'Anwesenheit' describes only the state of someone being physically there. The word sounds somewhat more formal and fits well in contexts such as school, work, appointments, or checks. They can be confused when someone is present somewhere. If the only important point is that the person is there, 'Anwesenheit' fits. If the coming or visiting is important, 'Besuch' fits.

Bei der Prüfung ist die Anwesenheit aller Teilnehmer wichtig.
During the exam, the presence of all participants is important.
Morgen ist ein Besuch im Büro geplant.
A visit to the office is planned for tomorrow.