die Mutter
mother
The female person who has given birth to or adopted a child and raises it.
Meine Mutter kommt am Wochenende zu Besuch.
My mother is coming to visit this weekend.

mother / nut
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mother
The female person who has given birth to or adopted a child and raises it.
Meine Mutter kommt am Wochenende zu Besuch.
My mother is coming to visit this weekend.

The meaning of 'Mutter' (mother / nut) depends heavily on the context. In a family setting, it is the female parent. In a technical context, often together with 'Schraube' (screw), it refers to a metal part.
Seine Mutter ist eine bekannte Ärztin.
His mother is a well-known doctor.
'Mutter' (mother) is the base word for many important terms. These include, for example, 'Muttersprache' (native language, the first language one learns) or 'Schwiegermutter' (mother-in-law, the mother of one's spouse).
Deutsch ist nicht meine Muttersprache.
German is not my native language.
In connection with family, there are fixed expressions. 'Mutter werden' means to become a mother, and a 'werdende Mutter' is a pregnant woman.
Meine ältere Schwester wird bald Mutter.
My older sister will soon become a mother.
The figurative meaning 'Ursprung' (origin) is used almost only in fixed idioms and proverbs. A very well-known one is: 'Die Not ist die Mutter der Erfindung' (necessity is the mother of invention).
Diese Niederlage wurde später als „die Mutter aller Krisen“ bezeichnet.
This defeat was later described as 'the mother of all crises.'
father
'die Mutter' and 'der Vater' both refer to a child's parents. The difference is gender: the mother is the female parent, and the father is the male parent. The words can be confusing for learners because they appear in the same family context and have different articles: 'die Mutter', but 'der Vater'. In everyday situations, both are often used together, for example when talking about family, upbringing, or parents.

Meine Mutter ruft mich jeden Sonntag an.
My mother calls me every Sunday.
Der Vater bringt seine Tochter morgens zur Schule.
The father takes his daughter to school in the morning.