grief / mourning
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grief
A deep feeling of pain and sorrow, usually triggered by the death of someone close or another serious loss.
Nach dem Tod ihres Hundes war sie von tiefer Trauer erfüllt.
After the death of her dog, she was filled with deep grief.
'Die Trauer' (grief/mourning) is the noun related to the verb 'trauern' (to grieve/mourn) and the adjective 'traurig' (sad). All of these words describe the feeling of great pain and loss.
Er ist sehr traurig, weil sein Freund weggezogen ist.
He is very sad because his friend moved away.
You can often recognize the meaning 'period of mourning' from verbs like 'tragen' (to wear/bear, in the sense of wearing mourning clothes) or from time expressions like 'Trauerjahr' (year of mourning). Without this context, the feeling is usually meant.
Ihre Trauer war für alle sichtbar.
Her grief was visible to everyone.
To indicate the reason for grief, German uses 'über' (+ accusative) for an event or 'um' (+ accusative) for a lost person or thing.
Ihre Trauer über den Verlust ihres Arbeitsplatzes war groß.
Her grief over the loss of her job was great.
Common expressions are 'in tiefer Trauer sein' (to be in deep grief) or 'seine Trauer verarbeiten' (to process one's grief). The feeling is often described as 'tief' (deep) or 'groß' (great).
Es braucht Zeit, die Trauer nach einem schweren Verlust zu verarbeiten.
It takes time to process the grief after a serious loss.
joy
'Freude' and 'Trauer' are opposite feelings. 'Freude' describes happiness and satisfaction. 'Trauer' describes deep pain and sorrow, often after the death of someone close or after a serious loss. 'Trauer' can also mean the period during which someone mourns. Use 'Freude' when something makes someone happy, and 'Trauer' when someone is processing a serious loss.
Nach dem Tod ihres Großvaters brauchte Selma Zeit für ihre Trauer.
After her grandfather's death, Selma needed time for her grief.
Dem Kind machte das neue Fahrrad große Freude.
The new bicycle brought the child great joy.