außer
except
As a preposition with the dative that indicates an exception; 'excluding'.
Alle waren da, außer meiner Schwester.
Everyone was there except my sister.

except / besides
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except
As a preposition with the dative that indicates an exception; 'excluding'.
Alle waren da, außer meiner Schwester.
Everyone was there except my sister.

The word 'außer' (except/outside) is derived from 'aus' (out) and originally means 'outside'. This origin helps explain its main meaning of 'excluded' or 'not included'.
Alle sind im Haus, außer dem Hund, der ist draußen im Garten.
Everyone is in the house except the dog; it's outside in the garden.
When 'außer' (except) is used as a preposition to name an exception, the following noun or pronoun is always in the dative. This is a fixed rule.
Außer dir kann mir niemand helfen.
No one except you can help me.
The expression 'außer Betrieb' (out of service) is used for technical devices, machines, or facilities that temporarily do not work or cannot be used.
Die Rolltreppe ist schon wieder außer Betrieb.
The escalator is out of service again.
The idiom 'außer sich sein' (to be beside oneself) describes a state of extreme emotional agitation. The reason is often given with 'vor' + dative.
Sie war außer sich vor Wut, als sie die Lüge entdeckte.
She was beside herself with anger when she discovered the lie.
As a conjunction, 'außer' (except) introduces a subordinate clause, often with 'dass' or 'wenn'. 'Außer dass' (except that) introduces a subordinate clause with the verb at the end, while 'außer wenn' (except if/unless) formulates a condition.
Ich weiß nichts über ihn, außer dass er in Berlin wohnt.
I know nothing about him, except that he lives in Berlin.
without
'ohne' and 'außer' can both express that something is not included. 'ohne' says that something is missing or not present. 'außer' names an exception within a group. With 'ohne Kaffee' (without coffee), there is no coffee. With 'alle außer mir' (everyone except me), everyone is included, only I am not. Learners confuse the words because in both cases something is excluded. The simple guideline is: 'ohne' describes an absence, while 'außer' describes an exception.

Am Bahnhof sind alle ausgestiegen außer der Kundin.
At the train station, everyone got off except the customer.
Im Urlaub warst du drei Tage ohne Internet.
On vacation, you went three days without internet.