Have to

We can use have to + infinitive, must + infinitive and should + infinitiveto express obligation (something you have to do).

Present	Positive	Negative
have to / don’t have to	strong obligation (possibly from outside) Children have to go to school. (sometimes ‘have got to’)	no obligation I don’t have to work on Sundays. You don’t have to eat anything you don’t like.
must / mustn’t	strong obligation (possibly based on the speaker’s opinion) I must study today.	negative obligation You mustn’t smoke here.
should / shouldn’t	mild obligation or advice You should save some money.	mild negative obligation or advice You shouldn’t smoke so much.

Be careful about the difference between mustn’t and don’t have to!
Mustn’t means it’s not allowed, or it’s a bad idea:

• You mustn’t eat so much chocolate, you’ll be sick

Don’t have to means you don’t need to do something, but it’s fine if you want to do it:

• I don’t have to get up early at the weekend
  (of course, if I want to get up early, that’s fine, but I can stay in bed if I want

Have to a menudo usamos  para expresar una obligación que se impone a la persona que habla. Por ejemplo;

• I have to be home at 10 o’clock. ( dice la hija o hijo de los padres)
• I have to go to the dentist later. (Tengo una cita)

have to o have got to
Have got to es más informal que have to.

• I have to leave now.  ---> I’ve got to leave now. - Tengo que salir ya.

Solo usamos have got to en el presente. Para el futuro y el pasado se usa have to.

• We will have to finish the work next week. - Tendremos que terminar el trabajo la próxima semana.
• We had to finish the work as soon as possible. - Tuvimos que terminar el trabajo tan pronto como sea posible.

do not have to = don’t have to. Se usa cuando no es necesario hacer algo.

• I don’t have to cook today. There’s plenty of food left over. - No tengo que cocinar hoy. Hay un montón de comida sobrante.
• You don’t have to visit them today. You can go tomorrow. - No tienes que visitarles hoy. Puedes ir mañana.

Need to

need not = needn’t. Otra forma de decir que no es necesario hacer algo

• I needn’t wash the car. It isn’t dirty. - No es necesario que limpie el coche. No está sucio.

También podemos decirlo así

• I don’t need to wash the car. It isn’t dirty.

La forma impersonal es; It’s not necessary - No es necesario / No hace falta

• It's not necessary for everyone to be there at 9 o’clock. -  No hace falta que estén todos allí a las nueve.

Needn’t have + past participle  Lo usamos para decir que alguien hizo algo, pero no era necesario hacerlo.

• I needn’t have made so much food for the the party, there is still a lot left.  (I did make a lot of food!) Nota: there is still a lot left. = Todavía queda mucha.
• I needn’t have washed the car. It wasn’t dirty. - No tenía por qué haber limpiado el coche. No estaba sucio.