aneinander
together
Expresses that things or people are located directly next to each other, often with contact.
Die Stühle standen dicht aneinander gereiht.
The chairs were lined up close together.

together / against each other
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together
Expresses that things or people are located directly next to each other, often with contact.
Die Stühle standen dicht aneinander gereiht.
The chairs were lined up close together.

The word is made up of the preposition 'an' (at/on) and the reciprocal pronoun 'einander' (each other). So it literally means 'an einander' (at/on each other) or 'in contact with each other.'
Die beiden Häuser sind sehr nah aneinander gebaut.
The two houses are built very close together.
'Aneinander' is often combined with verbs of position or movement. Typical examples are 'aneinander lehnen' (to lean against each other), 'aneinander kleben' (to stick to each other), or the idiom 'aneinander vorbeireden' (to talk past each other), when two people do not understand each other.
In der vollen U-Bahn mussten die Menschen dicht aneinander stehen.
In the crowded subway, people had to stand close together.
The expression 'aneinander geraten' (to clash/get into conflict) is a fixed idiom and means to begin an argument or conflict. It is always used in this context.
Wegen einer Kleinigkeit sind die Nachbarn gestern lautstark aneinander geraten.
The neighbors got into a loud argument yesterday over a small matter.
In combination with 'reihen' (to line up), 'aneinander' forms the separable verb 'aneinanderreihen' (to string together). In a main clause, 'aneinander' stands at the end; in a subordinate clause, it stays together with the verb.
Der Autor reiht ein Klischee an das andere aneinander.
The author strings one cliché after another together.
together
'zusammen' and 'aneinander' can both express closeness. 'zusammen' usually means that people do something together or that things are seen as a group. 'aneinander' is more precise when things or people have direct contact or are lying very close together. The words can be confused because both are the opposite of separation. But 'zusammen' is more about the question: Are they doing it together? 'aneinander' is more about the question: Are they touching or lying directly next to each other?

Im Supermarkt stehen die Einkaufswagen dicht aneinander.
In the supermarket, the shopping carts are standing close together.
Alina fährt morgens zusammen mit ihrer Freundin zur Schule.
Alina goes to school with her friend in the morning.