MUST/HAVE TO/ MUST NOT/ DON'T NEED TO

Must express obligation and a strong necessity, it is followed by a verb without "to".
Have to is an equivalent of Must but not as strong.
Examples :

• 
  Muslims must pray (perform salah) five times a day.
• 
  Students have to do their homework.

Must not or Mustn't expresses prohibition, something forbidden to do.
Examples :

• 
  You must not sit on grass.
• 
  You mustn't smoke in a cinema.

Needn't or don't/doesn't have to express the lack of necessity, something which is not necessary.
Examples :

• 
  You needn't buy bread. We have plenty.
• 
  You don't have to buy bread.

Must also expresses a logical conclusion.
Examples :

• 
  Rachel is absent from school today. She must be ill.
• 
  You must be kidding me.