
sich etwas wünschen
to wish for
To have a wish or desire for something that one would like to receive or achieve.
Zu meinem Geburtstag wünsche ich mir ein neues Buch.
For my birthday, I wish for a new book.
to wish
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to wish for
To have a wish or desire for something that one would like to receive or achieve.
Zu meinem Geburtstag wünsche ich mir ein neues Buch.
For my birthday, I wish for a new book.

to wish someone
To express hope for something good or positive toward another person.
Ich wünsche Ihnen ein schönes Wochenende!
I wish you a nice weekend!

to would like
A polite and formal way to ask about a person's desire or wish, often in the service sector.
Was wünschen Sie zu trinken?
What would you like to drink?
To express a wish that does not correspond to reality, 'wünschen' (to wish) is often used in the subjunctive II ('ich wünschte' (I wish)). The subordinate clause that describes the wish is then also in the subjunctive II.
Ich wünschte, ich könnte besser Klavier spielen.
I wish I could play the piano better.
When you wish for something for yourself, the verb is reflexive. The structure is: subject + sich (dative) + desired thing (accusative).
Sie wünscht sich ein Fahrrad zum Geburtstag.
She wishes for a bicycle for her birthday.
When you wish another person something good, you need a dative object (the person) and an accusative object (the good thing).
Wir wünschen unseren Nachbarn einen schönen Urlaub.
We wish our neighbors a nice vacation.
In the service sector, the question 'Was wünschen Sie?' (What would you like?) is used to ask about a customer's wishes in a particularly polite and formal way.
Guten Tag, was wünschen Sie? – Ich hätte gern einen Kaffee.
Good day, what would you like? – I'd like a coffee.
to hope
Hoffen and wünschen both express that you would like something to happen. When you hoffen, you consider the positive outcome possible. Sich etwas wünschen, on the other hand, refers to the desire itself and can also refer to something whose fulfillment is very unlikely.

Ohne genug Geld wünsche ich mir trotzdem ein Haus am Meer.
Even without enough money, I still wish for a house by the sea.
Nach der Kreditzusage hoffe ich, bald ein Haus am Meer kaufen zu können.
After getting the loan approval, I hope I’ll soon be able to buy a house by the sea.