The difference between "不 Bù" and “没 Méi” in Mandarin.

A
“不” 
1. is used to express personal wishes; 
For instance: 他不想去上班 Tā bùxiǎng qù shàngbān.  He doesn't want to go to work.

Note: When "不" is used in the past situation, it usually means that the person didn't want to or didn't willing to do something;
For instance: 昨天是他自己不去  Zuótiān shì tā zìjǐ bú qù. It's him that didn't (want to) go yesterday.

2. is used to deny recurrent or habitual situations;
For instance: 他不吸烟 Tā bù xīyān. He doesn't smoke.

“没”
is used to deny an action has occurred;
For instance: 我没在吃饭 Wǒ méi zài chīfàn. I'm not eating.

B
“不” 
is used to represent judgment or cognition：不是 búshì、不像 búxiàng/不会 búhuì、不应该 bù yīnggāi/不知道 bù zhīdào；
For instance: 他不是这种人 Tā búshì zhè zhǒng rén. He is not this kind of person. 

C
“不” 
is used to deny the nature or the state of things;
For instance: 这些苹果不红 Zhèxiē pínggǔo bù hóng. These apples are not red.

"没"
is used to deny the change of the nature or the state of things;
For instance: 这些苹果还没红 Zhèxiē pínggǔo hái méi hóng. These apples are still not red.