Many students ask me why the negative of “can” is “cannot ” but the negative of “could” is not “*couldnot”.
In British English, the single form “cannot” is used, while in American English, you can use both “cannot” and “can not”, though “cannot” is more common.
The contraction for both “cannot” and “can not” is “can’t”.
In summary, “cannot” is, by far, more usual and it’s the one I’d recommend you use. Having said that, there some cases when it’s necessary to use the form “can not”. When?

♥ When it’s used for emphasis.
No, you can not go out on New Year’s Eve. You’re only fourteen!

♥ When “not” is part of another construction as in, for example, the rather formal structure,” not only…. but (also)”
She can not only play the piano but also the violin

I hope to have answered your questions!