No or not?

No and not are the two most common words we use to indicate negation. We use no before a noun phrase:

We use not with any other phrase or clause:

It’s not often that you stop and think about the way you breathe.
Not suitable for children under 15.
Not surprisingly, it was a tense match but eventually the more experienced Australians won.
A: Do you go cycling all year round?
B: Not in the winter.
Not: ~~No in the winter~~.

No or not any?

There is very little difference in meaning between There is/are no + noun and There isn’t/aren’t any + noun:

There’s no reason to be afraid of her. (or There isn’t any reason to be afraid of her.)
There are no eggs in the fridge. (or There aren’t any eggs in the fridge.)

No + noun often makes the negative stronger. In speaking, we often stress no.

Compare

He paid no attention to what I was saying. (stronger)	He did*n’t* pay *any* attention to what I was saying.
I’ve decided that I have no alternative. (stronger)	I’ve decided that I do*n’t* have *any* alternative.

When a noun has an ungradable meaning (it is either something or it is not) we cannot use no + noun:

When a noun has a gradable meaning, no + noun means the same as not a/an + noun:

[a football manager talking about signing a new player]
It’s no secret that we are interested. (= It’s not a secret. A secret is gradable. Something can be more of a secret than something else.)

We often use no to respond to a yes-no question, or to agree with a negative statement. We don’t use not on its own in this way:

We use no and not in some common fixed expressions: