der Algerier
Algerian
A male person who comes from Algeria or has Algerian citizenship.
Mein neuer Kollege ist Algerier und lebt seit fünf Jahren in Deutschland.
My new colleague is Algerian and has lived in Germany for five years.

Algerian
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Algerian
A male person who comes from Algeria or has Algerian citizenship.
Mein neuer Kollege ist Algerier und lebt seit fünf Jahren in Deutschland.
My new colleague is Algerian and has lived in Germany for five years.

Terms for people of a nationality are often derived from the country name in German. 'Der Algerier' (the Algerian) comes from the country 'Algerien' (Algeria) and follows the pattern where the ending '-er' is added for the masculine form.
Er kommt aus Algerien, er ist also Algerier.
He comes from Algeria, so he is Algerian.
You have to distinguish between the noun 'der Algerier' (the Algerian; a person) and the adjective 'algerisch' (Algerian; a characteristic). The noun refers to the person themself, while the adjective describes something that comes from Algeria.
Er ist Algerier.
He is Algerian.
When using the verb 'sein' (to be) to state a person's nationality, the noun is usually used without an article. You say: 'Er ist Algerier' (He is Algerian), not 'Er ist ein Algerier' (He is an Algerian).
Der berühmte Schriftsteller Albert Camus war Algerier.
The famous writer Albert Camus was Algerian.
Arab / Arabian
'Araber' and 'Algerier' can both refer to a person from the Arabic-speaking world. But the difference is important: 'Algerier' specifically says that a man comes from Algeria or has Algerian citizenship. 'Araber' is broader and refers to Arab descent, Arab countries, or Arabic as a native language. Not every Arab is Algerian, and when referring to a specific nationality, 'Algerier' is more precise. The words can be confused because Algeria is an Arabic-speaking country.

Er ist Algerier und besucht seine Familie jeden Sommer in Algier.
He is Algerian and visits his family in Algiers every summer.
Der neue Nachbar ist Araber und spricht zu Hause Arabisch.
The new neighbor is Arab and speaks Arabic at home.