allgemein
general
Concerning all or most people or things; valid for everyone and not limited to a specific case.
Rauchen ist in öffentlichen Gebäuden allgemein verboten.
Smoking is generally prohibited in public buildings.

general
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general
Concerning all or most people or things; valid for everyone and not limited to a specific case.
Rauchen ist in öffentlichen Gebäuden allgemein verboten.
Smoking is generally prohibited in public buildings.

The word is made up of 'all' (all) and 'gemein'. Here, 'gemein' does not mean 'mean' or 'nasty', but rather 'shared' or 'common', as in the word 'Gemeinde' (community/municipality). So 'allgemein' literally means 'shared by all'.
Das ist eine Frage von allgemeinem Interesse.
That is a question of general interest.
The expression 'im Allgemeinen' (in general) is a fixed adverbial phrase and means 'normally'. If it stands at the beginning of a sentence, the verb follows in position two (inversion).
Im Allgemeinen schließt das Geschäft um 18 Uhr.
In general, the shop closes at 6 p.m.
Common combinations are 'allgemein bekannt' (generally known), 'allgemein gültig' (generally valid), or 'allgemein zugänglich' (generally accessible). It also occurs in fixed terms such as 'allgemeine Geschäftsbedingungen' (general terms and conditions, AGB) or 'der allgemeine Wille' (the general will).
Es ist allgemein bekannt, dass Sport gesund ist.
It is generally known that exercise is healthy.
In the meaning of 'not specific', 'allgemein' (general) is often used in a critical context, frequently intensified with 'zu' (too). A statement is then 'zu allgemein' (too general) to be useful.
Seine Antwort war mir zu allgemein, ich brauche mehr Details.
His answer was too general for me; I need more details.
at all / generally
'überhaupt' and 'allgemein' can both express that you are not talking about just one individual case. 'überhaupt' is an adverb and is often used to look at a topic in a basic or very broad way. 'allgemein' can describe something as an adjective that affects many or everyone, or in the phrase 'im Allgemeinen' it can mean 'usually'. There is a risk of confusion because both can express a general view. As a practical rule: 'im Allgemeinen' works well for 'normally', while 'überhaupt' fits better when you are making a general remark or strongly emphasizing a statement.

Im Allgemeinen planen wir unsere Termine eine Woche vorher.
In general, we plan our appointments a week in advance.
Warum braucht ihr überhaupt so viel Geld für den Kurs?
Why do you need so much money for the course in the first place?