
über
above / over
Indicates a position above something, without direct contact.
Die Lampe hängt über dem Tisch.
The lamp is hanging above the table.
over / about
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above / over
Indicates a position above something, without direct contact.
Die Lampe hängt über dem Tisch.
The lamp is hanging above the table.

over / across
Describes movement from one side to the other; across.
Wir fahren über die Brücke.
We're driving over the bridge.

about
Indicates the topic of a conversation, book, or thought.
Wir haben lange über deine Idee gesprochen.
We talked about your idea for a long time.

over / more than
Indicates that an amount or value is exceeded; more than.
Das Konzert hatte über tausend Besucher.
The concert had over a thousand visitors.

over
Refers to a period of time that is filled by an action.
Über das Wochenende verreisen wir.
We're going away over the weekend.

via / through
Indicates a medium or channel through which something happens; via.
Ich habe die Nachricht über das Internet erhalten.
I received the message via the internet.
'Über' is a two-way preposition. With a location (question: where?), the dative is used. With a direction (question: where to?), the accusative is used.
Das Bild hängt über dem Sofa.
The picture is hanging above the sofa.
In most non-spatial, that is figurative, meanings, 'über' is used with the accusative. This applies when it indicates a topic, an amount, or a period of time.
Wir reden über den neuen Film.
We're talking about the new film.
To indicate the topic of a conversation, text, or thought, 'über' is often combined with verbs of speaking, thinking, or feeling. Examples are: sprechen über (to talk about), lachen über (to laugh about/at), sich ärgern über (to be annoyed about), nachdenken über (to think about).
Die Kinder lachen über den Witz.
The children are laughing at the joke.
When 'über' means 'mehr als' (more than), it stands directly before a number or an amount. It is frequently used in news and reports.
Er wartete über eine Stunde auf den Bus.
He waited over an hour for the bus.
To describe a period of time during which something happens, 'über' is used with the accusative. In everyday usage, 'über das' is often contracted to 'übers'.
Übers Wochenende habe ich meine Großeltern besucht.
Over the weekend, I visited my grandparents.
When 'über' has the meaning 'via', it describes the path or medium through which information or an action is transmitted.
Man kann die Rechnung bequem über das Smartphone bezahlen.
You can conveniently pay the bill via smartphone.
to / too / closed
With books or information, „zu“ and „über“ can refer to the same topic. „Zu“ associates the work more generally with a subject area, while „über“ more clearly names the topic as the content being discussed. Both are often possible, but the perspective is slightly different.

Wir suchen ein Buch über gesunde Ernährung.
We’re looking for a book about healthy eating.
Wir suchen ein Buch zu gesunder Ernährung.
We’re looking for a book on healthy eating.