der Einkauf
shopping
The act of buying goods, usually food or other everyday necessities.
Ich muss nach der Arbeit noch den Einkauf für das Wochenende erledigen.
I still have to do the weekend shopping after work.

shopping / purchasing
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shopping
The act of buying goods, usually food or other everyday necessities.
Ich muss nach der Arbeit noch den Einkauf für das Wochenende erledigen.
I still have to do the weekend shopping after work.

The noun 'der Einkauf' (shopping/purchasing) is derived directly from the separable verb 'einkaufen' (to shop). It describes either the act of shopping or the result of it, meaning the goods bought.
Am Samstag gehe ich immer für die ganze Woche einkaufen.
On Saturdays I always go shopping for the whole week.
Whether the action (meaning 1) or the purchased goods (meaning 2) is meant can often be recognized from the verb. Verbs like 'erledigen' (to take care of) or 'machen' (to do/make) refer to the action, while verbs like 'tragen' (to carry) or 'auspacken' (to unpack) refer to the goods.
Ich muss noch schnell den Einkauf machen.
I still have to quickly do the shopping.
When referring to the activity of shopping, the noun is often used with the verbs 'machen' (to do/make) or 'erledigen' (to take care of). The phrase 'zum Einkauf gehen' (to go shopping) is also very common.
Wir müssen am Wochenende einen großen Einkauf machen.
We have to do a big shopping trip on the weekend.
In a professional context, 'der Einkauf' (purchasing) refers to the department of a company that is responsible for procuring materials. People then often say 'im Einkauf arbeiten' (to work in purchasing).
Er arbeitet seit fünf Jahren im Einkauf unserer Firma.
He has worked in purchasing at our company for five years.
purchase
'der Kauf' and 'der Einkauf' can both have to do with buying goods. 'der Kauf' is more general and can also mean a single larger or official purchase, for example the purchase of a car or an apartment. In everyday language, 'der Einkauf' often means shopping for groceries or other things you need regularly. In addition, 'der Einkauf' can also mean the goods bought, for example the bags after a trip to the supermarket. Learners confuse these words because both come from buying. For large or individual purchases, 'Kauf' sounds more natural; for supermarkets and everyday situations, 'Einkauf' is more likely.

Nach der Arbeit trägt Noah den Einkauf für die Familie in die Küche.
After work, Noah carries the family’s shopping into the kitchen.
Lisa spricht vor dem Kauf des Autos noch mit ihrer Bank.
Before buying the car, Lisa talks to her bank again.