zu
to
Expresses direction toward a place, a person, or a thing. It is used with the dative.
Ich gehe heute Abend zu meiner Freundin.
I'm going to my friend's place this evening.

to / too / closed
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to
Expresses direction toward a place, a person, or a thing. It is used with the dative.
Ich gehe heute Abend zu meiner Freundin.
I'm going to my friend's place this evening.

When 'zu' (to) expresses direction toward a person or place, it always requires the dative. The question for this is 'Zu wem?' (to whom?) or 'Wohin?' (where to?). Make sure to decline the article after 'zu' correctly.
Wir fahren am Wochenende zu unseren Großeltern.
We're driving to our grandparents' this weekend.
In usage, the preposition 'zu' (to) often contracts with the following article. 'Zu dem' becomes 'zum,' and 'zu der' becomes 'zur.' This is very common in both spoken and written language.
Ich gehe heute zum Arzt.
I'm going to the doctor today.
As an adverb, 'zu' (too) comes directly before an adjective or another adverb to express an excessive degree. It signals that a quality exceeds the desired or normal amount.
Dieser Kaffee ist mir zu stark.
This coffee is too strong for me.
'Zu' comes before the infinitive of a verb in many subordinate-clause constructions and after certain verbs. In sentences with 'um ... zu' (in order to), it introduces the purpose and stands directly before the infinitive at the end of the sentence.
Es ist wichtig, jeden Tag Deutsch zu lernen.
It's important to learn German every day.
In the meaning 'geschlossen' (closed), 'zu' behaves like a separable prefix. In a main clause, it stands at the end. It is often combined with verbs like 'sein' (to be) or 'machen' (to make/do).
Warum ist das Fenster zu?
Why is the window closed?
'Zu' is used to name an occasion or a meal. Typical phrases are 'zu Weihnachten' (for Christmas), 'zum Geburtstag' (for one's birthday), or 'zum Frühstück' (for breakfast).
Was gibt es heute zum Abendessen?
What's for dinner today?
The expression 'zu Hause' (at home) always describes a static location, so it answers the question 'Wo?' (where?). It means that someone is at the place where they live.
Er ist heute nicht im Büro, er arbeitet von zu Hause aus.
He's not in the office today; he's working from home.
The means of movement 'zu Fuß' (on foot) is a fixed expression. No article is used here, unlike with 'mit dem Auto' (by car) or 'mit dem Fahrrad' (by bicycle).
Da die U-Bahn nicht fährt, müssen wir zu Fuß gehen.
Since the subway isn't running, we have to go on foot.
To indicate a ratio, a mixing result, or a score, 'zu' is used. It stands between the two numbers or values being compared.
Mischen Sie Wasser und Saft im Verhältnis zwei zu eins.
Mix water and juice in a ratio of two to one.
so that / with it
'damit' and 'zu' can both express a purpose. The difference lies in the form of the sentence. 'damit' introduces a subordinate clause with its own subject and a conjugated verb. 'zu' comes before an infinitive, often in the form 'um ... zu' (in order to). Learners confuse the words because both can answer the question 'Warum?' (why?) or 'Wozu?' (what for?). A practical rule is: if a whole subordinate clause follows, 'damit' often fits. If only an infinitive follows, 'zu' or 'um ... zu' fits.

Frau Meier liest am Wochenende die Notizen, um sich auf die Prüfung vorzubereiten.
Ms. Meier reads the notes on the weekend to prepare for the exam.
Die Chefin erklärt den Plan langsam, damit alle ihn verstehen.
The boss explains the plan slowly so that everyone understands it.