Learn Swedish: Du måste stanna här.

Stanna is in its infinitive (dictionary) form. Whenever you use a modal verb like måste (must), the main verb that follows it takes the bare infinitive form. This means you drop the present tense -r and you don't use the word att (to) before it.

Doesn't the verb stanna mean "to stop"?

It actually means both "to stop" and "to stay"! You have to figure out which one it is from the context. If you are driving, it usually means "stop," but if someone is telling you where to wait, it means "stay."

If I want to say "You must not stay here," do I just say Du måste inte stanna här?

No, this is a very common trap! In Swedish, Du måste inte means "You don't have to" (it's not required). If you want to tell someone they are strictly not allowed to stay somewhere ("You must not"), you use the modal verb får instead: Du får inte stanna här (literally "You may not stay here").

Why do we use här instead of hit for "here"?