zuhause
at home
Indicates the place where someone lives; in one's own apartment or house.
Am Wochenende bleibe ich am liebsten einfach nur zuhause.
On weekends, I prefer to just stay at home.

at home
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at home
Indicates the place where someone lives; in one's own apartment or house.
Am Wochenende bleibe ich am liebsten einfach nur zuhause.
On weekends, I prefer to just stay at home.

The word 'zuhause' (at home) is a fixed combination of the preposition 'zu' and the noun 'Hause'. It is used as an adverb and describes a place. The spelling as one word, 'zuhause', is the common form today.
Nach einem langen Tag bin ich froh, wieder zuhause zu sein.
After a long day, I'm glad to be back home.
'Zuhause' (at home) is an adverb of place and answers the question 'Wo?' (Where?). It always describes a static place, meaning being in one's own apartment or house.
Wo bist du? – Ich bin schon zuhause.
Where are you? – I'm already at home.
A very common and important phrase is 'sich zuhause fühlen' (to feel at home). It means that you feel very comfortable and safe in a place, even if it is not your own home.
In ihrer neuen Wohnung hat sie sich sofort zuhause gefühlt.
She immediately felt at home in her new apartment.
In the figurative meaning, 'zuhause' (at home) is always used with the preposition 'in' and the dative. The fixed expression is 'in einem Thema zuhause sein' (to be at home in a subject), and it means that someone knows a lot about it.
Mein Professor ist in der Geschichte des Mittelalters wirklich zuhause.
My professor is truly at home in the history of the Middle Ages.
at home
'zuhause' and 'daheim' both mean that someone is at the place where they live. In many sentences, you can use both words almost the same way. 'zuhause' is very general and easily understood everywhere. 'daheim' often sounds a bit cozier or more personal and is used more often in some regions. If you simply want to say that you are not outside or on the way, 'zuhause' always works well. 'daheim' fits especially well when the place feels like a familiar home.

Heute bleibe ich zuhause, weil ich noch auf ein Paket warte.
Today I'm staying at home because I'm still waiting for a package.
Am Sonntag kochen wir daheim und laden meine Schwester ein.
On Sunday, we're cooking at home and inviting my sister over.