die Angst
fear
A strong, unpleasant feeling of threat or worry.
Bei dem Gedanken an die Prüfung spürte er große Angst.
At the thought of the exam, he felt great fear.

fear
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fear
A strong, unpleasant feeling of threat or worry.
Bei dem Gedanken an die Prüfung spürte er große Angst.
At the thought of the exam, he felt great fear.

The preposition after 'Angst haben' (to be afraid) is very important. 'Angst vor' (+ dative) describes the source of fear. 'Angst um' (+ accusative) expresses worry about someone or something.
Das Kind hat Angst vor der Dunkelheit.
The child is afraid of the dark.
Common verbs with 'Angst' (fear) are 'Angst haben' (to be afraid), 'Angst bekommen' (to suddenly feel afraid), and 'jemandem Angst machen' (to scare someone).
Als das Licht ausging, bekam ich große Angst.
When the light went out, I became very afraid.
To explain the reason for the fear more precisely, you can use a subordinate clause with 'dass' (that) or an infinitive construction with 'zu' (to).
Ich habe Angst, dass ich den Zug verpasse.
I'm afraid that I'll miss the train.
courage
'die Angst' and 'der Mut' are often opposites. 'Angst' is the unpleasant feeling you have when you feel threatened or are afraid of something. 'Mut' means doing something difficult or risky despite fear. So courage does not necessarily mean having no fear. Often, you show courage precisely when you feel fear and act anyway.

Vor der Prüfung spürt Lena große Angst.
Before the exam, Lena feels great fear.
Das Team hat den Mut, dem Chef ehrlich seine Meinung zu sagen.
The team has the courage to tell the boss its honest opinion.