When using the word 'promise' you are giving your word that what you are saying is true. You might also be assuring someone a guarantee that you will follow thru on what you are saying to them.

当使用'promise'这个词的时候，这就表明你说的话是真实的，你也可以向某人保证你会遵循你对他们说的话。

When using 'promise not to' you are stating you will not do a particular thing. 当用'promise not to'的时候你就表明你不会去做一件特别的事情。

Here are some examples: 这里有一些例子： 

"I promise not to tell."

 我保证不会说的。

"I promise not to leave without you."

 我保证不离开你。

"I promise not to be so late."

 我保证不会迟到太久。

"I promise not to hurt your feelings."

 我保证不会伤害你的感情。

"I promise not to wake you up."

 我保证不会叫醒你的。

You can also just use the word 'promise' to assure someone of your intentions. 你也可以只用'promise'这个词向别人确保你的意图。

Here are some examples: 这里有一些例子： 

"I promise I am telling the truth."

 我保证我说的都是真的。

"I promise to practice my math."

 我保证要练习数学。

"I promise to call you."

 我保证打电话给你。

"I promise I will tell you."

 我保证我将会告诉你。

"I promise I will come to your party."

 我保证我将会参加你的派对。