Local preposition 'an' (at/on, Wo?/where? + dative)

an means at / on a vertical surface or right beside something - a picture on the wall, a person at the window, a town on a river. As a two-way preposition, an takes the dative for a static position (question Wo?, no movement).

The rule:

• Wo? (position) → an + Dativ
• Wohin? (movement onto/towards) → an + Akkusativ

Dative articles after an: an dem (m/n), an der (f). The masculine/neuter form contracts: an dem → am.

Paired examples:

• Das Bild hängt an der Wand. - The picture hangs on the wall. (Wo? → Dativ)
• Ich hänge das Bild an die Wand. - I hang the picture on the wall. (Wohin? → Akkusativ)
• Wir sitzen am Tisch. - We are sitting at the table. (Wo? → Dativ, an dem → am)
• Er steht am Fenster. - He is standing at the window. (Wo? → Dativ)

Common mistakes:

• Confusing an (vertical surface / beside) with auf (horizontal surface).
• Using the accusative for a static position: Das Bild hängt an die Wand is wrong - say an der Wand.

'an' (at / on a vertical surface) takes the dative for a location (Wo?).

'an' takes the dative for location (Wo?); an dem → am.

'an' steht bei einer Ortsangabe (Wo?) mit dem Dativ.