einzeln
separately
Separate from one another; one person or thing after another, not together.
Die Schüler wurden gebeten, einzeln nach vorne zu kommen.
The students were asked to come to the front one at a time.

individual / separate
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separately
Separate from one another; one person or thing after another, not together.
Die Schüler wurden gebeten, einzeln nach vorne zu kommen.
The students were asked to come to the front one at a time.

The word 'einzeln' (individual / separate) is derived from the number 'eins' (one). It always describes something that relates to a single unit or person, or that is separate from others.
Jeder Gast bekommt ein einzelnes Stück Kuchen.
Each guest gets an individual piece of cake.
'Einzeln' can stand before a noun as an adjective and is then declined. But it can also be used as an adverb and then remains unchanged.
Jeder einzelne Gast hat ein Geschenk bekommen.
Every individual guest received a gift.
To emphasize that truly every single person or thing is meant, 'einzeln' (individual) is very often combined with 'jeder', 'jede', or 'jedes' (each/every). This combination strengthens the statement.
Ich habe jede einzelne Seite des Buches gelesen.
I read every single page of the book.
In the meaning 'wenige, verstreut' (a few, scattered), 'einzeln' is often used with plural nouns that normally occur in larger numbers. Typical examples are 'einzelne Fälle' (isolated cases), 'einzelne Häuser' (scattered houses), or 'einzelne Regentropfen' (individual raindrops).
Es gab nur einzelne Beschwerden, die meisten Kunden waren zufrieden.
There were only isolated complaints; most customers were satisfied.
together
'zusammen' and 'einzeln' are often opposites when people or things are viewed as a group or separately. 'zusammen' means that several people or things act together or as a group. 'einzeln' means that they are viewed separately from one another, one after another, or each on its own. For example, you might say that you pay together, but call out the names individually. So the difference is: as a group or separately.

Vor dem Termin hat Frau Becker die Unterlagen einzeln geprüft.
Before the appointment, Ms. Becker checked the documents one by one.
Für den Ausflug kaufen wir die Fahrkarten zusammen.
For the trip, we are buying the tickets together.