der Norweger
Norwegian
A male citizen of Norway or a male person of Norwegian origin.
Mein neuer Kollege ist Norweger und spricht fünf Sprachen.
My new colleague is Norwegian and speaks five languages.

Norwegian / Norwegian sweater
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Norwegian
A male citizen of Norway or a male person of Norwegian origin.
Mein neuer Kollege ist Norweger und spricht fünf Sprachen.
My new colleague is Norwegian and speaks five languages.

The word 'Norweger' (Norwegian) is derived directly from the country name 'Norwegen' (Norway). This pattern is found with many nationalities where the ending '-er' is added to the country stem.
Er kommt aus Norwegen, er ist also Norweger.
He comes from Norway, so he is Norwegian.
The context tells you whether a person or the sweater is meant. Verbs like 'sprechen' (to speak) or 'leben' (to live) point to the person. Verbs like 'tragen' (to wear), 'anziehen' (to put on), or adjectives like 'warm' point to the sweater.
Der Norweger, den ich gestern kennengelernt habe, wohnt in Oslo.
The Norwegian I met yesterday lives in Oslo.
When the sweater is meant, 'Norweger' (Norwegian sweater) is often combined with adjectives like 'warm' (warm), 'dick' (thick), or 'gestrickt' (knitted). Typical verbs are 'anziehen' (to put on) or 'tragen' (to wear).
Meine Oma hat mir einen warmen Norweger zu Weihnachten gestrickt.
My grandma knitted me a warm Norwegian sweater for Christmas.
Norwegian
'norwegisch' and 'der Norweger' both refer to Norway. However, they belong to different parts of speech. 'norwegisch' is an adjective and describes a language, a person, food, a city, or something from Norway. 'der Norweger' is a noun and means a man from Norway or a man of Norwegian origin. The words can be confused because they look similar and both have to do with nationality. The important point is: for qualities or characteristics, use 'norwegisch'; for a male person, say 'der Norweger'.

Im Restaurant sitzt ein Norweger am Fenster und liest die Speisekarte.
A Norwegian is sitting by the window in the restaurant and reading the menu.
Mein Kollege hat gestern ein norwegisches Gericht gekocht.
My colleague cooked a Norwegian dish yesterday.