die Woche
week
A period of seven consecutive days, usually from Monday to Sunday.
Nächste Woche fahre ich in den Urlaub.
Next week I’m going on vacation.

week
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week
A period of seven consecutive days, usually from Monday to Sunday.
Nächste Woche fahre ich in den Urlaub.
Next week I’m going on vacation.

With time expressions using 'Woche' (week), the adjectives 'diese' (this), 'nächste' (next), and 'letzte' (last) are used without a preposition. These expressions are in the accusative and function like an adverb in the sentence.
Letzte Woche war ich krank.
I was sick last week.
Prepositions are used to describe periods of time. 'In einer Woche' means a point in time in the future, 'vor einer Woche' means a point in time in the past, and 'seit einer Woche' means a duration that continues up to now.
In einer Woche beginnen die Ferien.
The holidays begin in a week.
To name a point in time within the week, people often use the combinations 'Anfang der Woche' (at the beginning of the week), 'Mitte der Woche' (in the middle of the week), and 'Ende der Woche' (at the end of the week).
Wir haben Anfang der Woche einen wichtigen Termin.
We have an important appointment at the beginning of the week.
The expression 'unter der Woche' refers to the working days from Monday to Friday. It is often used in contrast to 'am Wochenende' (on the weekend).
Unter der Woche habe ich wenig Zeit, aber am Wochenende können wir uns treffen.
During the week I have little time, but we can meet on the weekend.
weekend
'die Woche' and 'das Wochenende' are often opposites. 'die Woche' means either seven days or, in everyday language, especially the workdays from Monday to Friday. 'das Wochenende' usually means Saturday and Sunday, that is, the time after the workweek. When someone says 'unter der Woche' (during the week), they normally do not mean Saturday and Sunday. 'am Wochenende' (on the weekend) fits when talking about free time, rest, or plans for Saturday and Sunday.

Unter der Woche hat Frau Klein selten Zeit für lange Einkäufe.
During the week, Ms. Klein rarely has time for long shopping trips.
Das Wochenende ist frei, deshalb besucht Tom seine Eltern.
The weekend is free, so Tom is visiting his parents.