You may also know these verbs as “helping verbs” because that’s exactly what they do, help to convey the idea expressed by another verb.
There are six modal auxiliaries in German, here presented with their definitions and a rough English equivalent:
|dürfen||permission||to be allowed to, may|
|wollen||intention, desire||to want to|
|sollen||duty, expectancy||to have to, shall|
|müssen||necessity, compulsion||to have to, must|
|mögen||possibility||to possibly do, might|
|können||ability||to be able to, can|
These auxiliaries are almost always followed by infinitives. The infinitives never take zu.
Wir müssen es lernen.
We have to learn it.
Ich kann dieses Buch nicht verstehen.
I can’t understand this book.