mustn´t and needn´t

We use mustn´t when we mean "Do not do this"
We use needn´t when we mean "This is not necessary"

You mustn't do something = it is necessary that you do not do it (so don't do it):

• You must keep it a secret. You mustn't tell anybody else. (= don't tell anybody else)
• It's essential that nobody hears us. We mustn't make any noise.

You needn't do something = it is not necessary that you do it, you don't need to do it:

• You can come with me if you like but you needn't come if you don't want to. (= it is not necessary for you to come)
• We've got plenty of time. We needn't hurry. (= it is not necessary to hurry)

Examples with mustn´t and needn´t