beherrschen
to master
To be very good at a skill, body of knowledge, or language and use it confidently.
Sie beherrscht drei Fremdsprachen fließend.
She masters three foreign languages fluently.

to master / control / dominate
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to master
To be very good at a skill, body of knowledge, or language and use it confidently.
Sie beherrscht drei Fremdsprachen fließend.
She masters three foreign languages fluently.

'Beherrschen' derives from 'der Herr' (the lord/master) and 'herrschen' (to rule). The prefix 'be-' makes the verb transitive, so it always needs an accusative object. The basic idea is to have full control over something.
Ein guter Reiter beherrscht sein Pferd.
A good rider controls his horse.
The meaning changes completely depending on whether the verb is reflexive or not. 'Sich beherrschen' means to control one's own feelings. 'Etwas beherrschen' means to master a skill or rule/control an area.
Er war so wütend, dass er sich kaum beherrschen konnte.
He was so angry that he could hardly control himself.
In the meaning of 'etwas können' (to be able to do something), 'beherrschen' is often combined with skills and knowledge: 'eine Sprache beherrschen' (to master a language), 'ein Instrument beherrschen' (to master an instrument), 'eine Methode beherrschen' (to master a method), or 'ein Handwerk beherrschen' (to master a craft).
Mein Großvater beherrscht das Handwerk des Schreinerns.
My grandfather has mastered the craft of carpentry.
'Sich beherrschen' is often used in situations where someone suppresses strong emotions. Common phrases include 'sich nicht mehr beherrschen können' (to no longer be able to control oneself) or 'sich nur mit Mühe beherrschen' (to control oneself only with difficulty).
Als sie die Beleidigung hörte, konnte sie sich nicht mehr beherrschen.
When she heard the insult, she could no longer control herself.
Whether 'beherrschen' means 'regieren' (to rule) or 'dominieren' (to dominate) depends on the object. If it refers to people or a country, it means 'regieren' (to rule). If it refers to a landscape, a topic, or a discussion, it has the figurative meaning 'dominieren' (to dominate).
Die Diskussion wurde von einem einzigen Thema beherrscht.
The discussion was dominated by a single topic.
to be able to
'können' and 'beherrschen' can both describe an ability. 'können' is the normal, general word: you have an ability or have learned something. 'beherrschen' is stronger and means that you can do something very well and confidently. Learners may confuse the words because both fit with languages, techniques, or tasks. If you only want to say that someone can do something, use 'können'. If you want to emphasize that someone really has it under control, 'beherrschen' fits better.

Nach dem Kurs beherrscht er die wichtigsten Regeln der deutschen Grammatik.
After the course, he has mastered the most important rules of German grammar.
Am Morgen hat sie für ihre Familie schon ein einfaches Frühstück machen können.
In the morning, she was already able to make a simple breakfast for her family.