einsam
lonely
The negative feeling of being alone and without social contacts; feeling separated from others.
Obwohl er viele Bekannte hatte, fühlte er sich oft einsam.
Although he had many acquaintances, he often felt lonely.

lonely / remote
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lonely
The negative feeling of being alone and without social contacts; feeling separated from others.
Obwohl er viele Bekannte hatte, fühlte er sich oft einsam.
Although he had many acquaintances, he often felt lonely.

The word consists of 'ein' (one) and the suffix '-sam', which describes a quality or tendency. 'Einsam' (lonely) therefore describes the state or feeling of being alone.
Nach dem Umzug fühlte er sich in der neuen Stadt sehr einsam.
After the move, he felt very lonely in the new city.
The meaning of 'einsam' (lonely / remote) depends on the context. If it refers to a person and their feelings, it means 'lonely'. If it describes a place, it means 'remote' or 'deserted'.
Er ist ein einsamer Mensch, der nur wenige Freunde hat.
He is a lonely person who has only a few friends.
When referring to the feeling, 'einsam' (lonely) is often combined with verbs like 'sich fühlen' (to feel), 'sein' (to be), or 'werden' (to become). A typical phrase is 'sich einsam fühlen' (to feel lonely).
Im Alter werden viele Menschen einsam.
In old age, many people become lonely.
When describing a place, 'einsam' (remote / deserted) often comes before nouns like 'Insel' (island), 'Strand' (beach), 'Hütte' (cabin), 'Gegend' (area), or 'Tal' (valley).
Der Wanderweg führte durch ein einsames Tal.
The hiking trail led through a remote valley.
alone / only
'allein' and 'einsam' both have to do with the absence of other people. But 'allein' first describes only the situation: a person is without other people. That can be neutral, good, or bad. 'einsam' describes a negative feeling: you feel abandoned or wish you had more contact. Learners often confuse the words because you can be lonely when you are alone. But not everyone who is alone is also lonely.

Seit dem Umzug fühlt sich Tom oft einsam, weil er hier noch niemanden kennt.
Since the move, Tom often feels lonely because he doesn't know anyone here yet.
Heute Abend bin ich allein zu Hause und lese in Ruhe ein Buch.
Tonight I am home alone and reading a book in peace.