
neben
next to
Indicates a position directly at the side of something (where?). Used with the dative.
Die Apotheke ist direkt neben der Post.
The pharmacy is right next to the post office.
next to / besides
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next to
Indicates a position directly at the side of something (where?). Used with the dative.
Die Apotheke ist direkt neben der Post.
The pharmacy is right next to the post office.

next to
Indicates movement to a place directly at the side of something (to where?). Used with the accusative.
Setz dich doch bitte neben mich.
Please sit down next to me.

besides
Means 'in addition to' or 'apart from'.
Neben seiner Arbeit als Lehrer schreibt er auch Bücher.
Besides his work as a teacher, he also writes books.

to be out of it
Colloquial for being confused, unfocused, or not oneself.
Nach der langen Nacht war er am nächsten Tag völlig neben der Spur.
After the long night, he was completely out of it the next day.

compared to
Expresses a comparison; in relation to.
Neben einem professionellen Sportler wirkt mein Training wie ein Kinderspiel.
Compared to a professional athlete, my training seems like child's play.
In its spatial meaning, 'neben' (next to) is a two-way preposition. The question 'Wo?' (where?) takes the dative, while the question 'Wohin?' (to where?) takes the accusative.
Dein Schlüssel liegt neben dem Buch. (Wo? -> Dativ)
Your key is lying next to the book. (Where? -> dative)
While the spatial meaning of 'neben' (next to) can take the dative or accusative, the figurative meanings 'zusätzlich zu' (in addition to) and 'im Vergleich zu' (compared to) always require the dative.
Neben dem Studium hat er keine Zeit für Hobbys.
Besides his studies, he has no time for hobbies.
In the meaning 'zusätzlich zu' (in addition to), 'neben' (besides) often introduces a secondary thought or additional information. It frequently appears at the beginning of a sentence, followed by the dative.
Neben Deutsch spricht sie auch fließend Spanisch und Englisch.
Besides German, she also speaks fluent Spanish and English.
The idiom 'neben der Spur sein' (to be out of it) is colloquial. It means that someone is unfocused, confused, or not in their normal form.
Ich habe schlecht geschlafen und bin heute total neben der Spur.
I slept badly and am totally out of it today.
When 'neben' (compared to) expresses a comparison, it places two things in relation to each other. It is often used to emphasize a strong contrast.
Neben seiner riesigen Villa sieht unser Haus winzig aus.
Compared to his huge villa, our house looks tiny.
to / too / closed
In a request to sit down, „zu“ indicates joining a person or group. „Neben“, on the other hand, specifies the exact place directly beside someone. Choose „neben“ when the immediate seating position is important.

Setz dich bitte neben Anna an den Tisch.
Please sit next to Anna at the table.
Setz dich bitte zu Anna an den Tisch.
Please sit with Anna at the table.