[subject] + 没有 + [noun] [subject] + 没(有) + [verb]
Before a noun it can shorten to méi没: 我没钱 and 我没有钱 say the same thing, the shorter one more casually.
In front of a verb, 没 or 没有 says the event did not take place. This is how you negate a completed action; 不 has no version of it.
Both translate as "not". 没 reports that something did not occur; 不 says it is not the case, not wanted, or not going to happen.
Swapping them changes the sentence. 我不去 refuses; 我没去 reports.
A sentence with 了 after the verb loses it when 没 arrives: the completion marker and the "it didn't happen" marker cannot both be there.
过 stays: 我没去过北京 is correct, because 过 is about experience rather than completion.