hate
noun 
an extremely strong dislike 
She gave him a look of pure hate. [U]
The feelings of hate grew stronger every day. [U]
One of my pet hates (=one of the main things I dislike) is people who use your name all the while when they're speaking to you. [C]
See also hatred.

If someone receives hate mail they get unpleasant or cruel letters from someone who dislikes them. 

hate
verb 
Kelly hates her teacher. [T]
She hated the cold dark days of winter. [T]
I hate it when you do that. [T]
I have always hated speaking in public. [+ v-ing]
I hate him telling me what do to all the time. [+ obj + v-ing]
I hate (=do not want) to interrupt, but it's time we left. [+ to infinitive]
I'd hate (=would not like) you to think I didn't appreciate what you'd done. [+ obj + to infinitive]
In this terrible conflict how can we avoid the children learning to hate? [I]

(informal) Children sometimes say that they hate someone's guts, meaning that they really do hate them. 
Tell Harry from me that I hate his guts!

hated
adjective 
He was the most hated teacher in the school.
Reluctantly she put on the hated shoes.

hateful
adjective 
DATED 
Hateful means very unpleasant. 
I never wear grey because it reminds me of my hateful school uniform.

hatefulness
noun [U] 

-hater
combining form 
I may be a feminist, but I'm certainly not some sort of man-hater.
He's a self-confessed woman-hater.

hatred
noun [U] 
Hatred is an extremely strong feeling of dislike. 
What is very clear in these letters is Clark's passionate hatred of his father.
The motive for this shocking attack seems to be racial hatred.
Orbach believes that the root cause of the so-called slimmer's disease is self-hatred and fear of rejection.