die Klage
complaint
The expression of dissatisfaction, pain, or grief about something. A complaint or lament.
Seine ständige Klage über die Arbeit nervt die Kollegen.
His constant complaining about work annoys his colleagues.

complaint / lawsuit
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complaint
The expression of dissatisfaction, pain, or grief about something. A complaint or lament.
Seine ständige Klage über die Arbeit nervt die Kollegen.
His constant complaining about work annoys his colleagues.

'Die Klage' (complaint/lawsuit) is the noun related to the verb 'klagen' (to complain/to sue). The preposition used with the verb helps you understand the meaning: 'über etwas klagen' (to complain about something) leads to 'Klage' as a complaint, while 'gegen jemanden klagen' (to sue someone) leads to 'Klage' as a court case.
Er klagt ständig über das Wetter.
He constantly complains about the weather.
You can recognize the difference between the meanings from the context. Words like 'Gericht' (court), 'Anwalt' (lawyer), or 'einreichen' (to file) point to the legal meaning. Words like 'Schmerz' (pain), 'Leid' (suffering), or 'ständig' (constant) point to the complaint meaning.
Ihre Klage über Kopfschmerzen wurde immer lauter.
Her complaint about headaches grew louder and louder.
When 'Klage' means a complaint, the reason for it is expressed with the preposition 'über' and the accusative.
Die Klage über den Lärm der Baustelle war berechtigt.
The complaint about the noise from the construction site was justified.
In a legal context, 'Klage' is often used with the verbs 'einreichen' (to file) or 'erheben' (to bring/file). The person or institution being sued is named with the preposition 'gegen' (against).
Der Verein hat Klage gegen die Entscheidung der Stadt eingereicht.
The association filed a lawsuit against the city's decision.
process / trial
'der Prozess' and 'die Klage' both belong to the area of court and law, but they do not mean the same thing. 'die Klage' is the legal action by which someone brings a dispute before a court. 'der Prozess' is then the court proceeding in which that dispute is decided. Learners may confuse the words because a 'Klage' often leads to a 'Prozess'. Practically speaking: you file a 'Klage' (lawsuit), and later it can turn into a 'Prozess' (trial / court proceeding).

Die Kundin reichte eine Klage ein, weil die Firma nicht zahlen wollte.
The customer filed a lawsuit because the company did not want to pay.
Der Prozess dauerte drei Monate, weil viele Zeugen gehört wurden.
The trial lasted three months because many witnesses were heard.