Learn Icelandic: Maðurinn vill sitja við gluggann. - The man wants to sit by the window.

While hjá implies being in the general vicinity of something (or near a person), við is used for very close proximity, attachment, or functional positioning. You sit við gluggann (right up against the window) or við borðið (at the table) because you are placed deliberately and closely at that specific boundary or object.

Since the man is sitting still, shouldn't the preposition take the dative case for location?

This is a very common trap! You likely remember that prepositions like í (in) and á (on) use the dative for staying still and the accusative for movement. However, við does not follow this "movement vs. stillness" rule. When við means "by" or "at" a physical location, it almost always takes the accusative case, regardless of whether there is motion or not.

How do we get "gluggann" from the dictionary form of the word for "window"?

The dictionary form is gluggi, which is a weak masculine noun (meaning it ends in a vowel). Because við forces it into the accusative case, the ending changes to an 'a', becoming glugga. To say "the" window, we attach the masculine accusative definite article -nn, resulting in gluggann.

Why doesn't the verb "vill" have a regular third-person ending?