
können
can / be able to
Expresses an ability or a learned skill.
Ich kann sehr gut schwimmen.
I can swim very well.
to be able to
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can / be able to
Expresses an ability or a learned skill.
Ich kann sehr gut schwimmen.
I can swim very well.

can
Expresses a possibility or an opportunity.
Wir können uns morgen treffen, wenn du Zeit hast.
We can meet tomorrow if you have time.

can / may
Used colloquially to give or ask for permission (instead of 'dürfen').
Kann ich kurz dein Handy benutzen?
Can I use your phone for a moment?

could / might
Expresses an assumption or logical conclusion, often in the subjunctive II (könnte).
Das Geräusch könnte von der Heizung kommen.
The noise could be coming from the heating.

know / master
Means to know something or have mastered something.
Er kann das ganze Gedicht auswendig.
He knows the whole poem by heart.
'Können' is a modal verb. In a main clause, it stands in position 2, and the second verb (the infinitive) stands at the end of the sentence.
Ich kann dich morgen vom Bahnhof abholen.
I can pick you up from the train station tomorrow.
Pay attention to the irregular conjugation in the present tense. In the singular forms (ich, du, er/sie/es), the vowel 'ö' changes to 'a'. The first and third person singular are identical: 'ich kann' (I can), 'er kann' (he can).
Er kann nicht kommen, weil er krank ist.
He can't come because he's sick.
When 'können' is used without a second verb but with a direct accusative object, it means 'etwas beherrschen' (to have mastered something) or 'etwas wissen' (to know something). This is often the case with languages, poems, or skills.
Sie kann fließend Spanisch.
She knows fluent Spanish.
In colloquial speech, 'können' is very often used to ask for permission. In more formal situations, 'dürfen' (may / to be allowed to) is more precise, but 'Kann ich...?' (Can I...?) is completely common in everyday life.
Kann ich mal kurz telefonieren?
Can I make a quick phone call?
The subjunctive II form 'könnte' (could / might) is used to express a possibility, an assumption, or a polite suggestion. It is weaker and less certain than the normal 'kann' (can).
Es könnte heute noch regnen.
It could still rain today.
to manage / create
“Können” and “schaffen” can both refer to completing a task by a deadline. “Können” asks about ability or possibility, while “schaffen” emphasizes that the task will actually be completed under the specific circumstances. For a deadline, “schaffen” is therefore often more precise.

Kannst du den Bericht bis morgen fertig schreiben?
Can you finish writing the report by tomorrow?
Schaffst du es, den Bericht bis morgen fertig zu schreiben?
Can you manage to finish writing the report by tomorrow?