"Hamburg is by the water."
Translation:Hamburg ist am Wasser.
We say cities are "am Wasser/Fluss/See/Teich"(=water, river, lake, small lake) and "am Meer, an der See" (sea, sea) when they are "near, by or nearby" the water. "an" is the normal preposicion for this.
- Hamburg ist an der Alster. Hamburg ist am Wasser.
- Köln ist/liegt am Rhein. Berlin ist/liegt an der Spree.
Is it more accurate to think of "neben" as being the sort of "side to side" type of next to, rather than just being "near each other?"
Something like that.
Also, am Wasser might mean "on either sides of the water" while neben dem Wasser could only mean "next to the water".
am is a contraction of an + dem, i.e. the preposition an and the neuter or masculine dative article dem.
If you contract an with the masculine accusative article das, you get ans, e.g. ans Wasser "to the water" (indicating the destination of motion, rather than a location).
ams does not exist; that would be *an + dem + das" with two articles in different cases and make no sense.
Is an and am basically short for auf+den & auf+dem?
Not in standard German.
an basically means "at" and am is a contraction of an dem "at the".
In Austrian German, am can be a contraction for not only an dem but also for auf dem. This usage is not accepted on this course.
an den, auf den, and auf dem do not have any contractions in the standard (written) language.
(In the spoken language, you may hear an'n, auf'n, and auf'm.)