I'd argue that any attempt at understanding mathematical notation universally will fail. Different fields and different sub-topics and different authors have vastly different conventions, for good reason.

Sure, one can perhaps expect that something that uses an integral sign shares some properties with ordinary integration of real functions, but to really understand what the notation entails, one really has to study the underlying material.

I feel that what you're asking for is kind of akin to wanting to read a novel in a foreign language using only a dictionary of the 10% most commonly used words of said language, with each entry resolving only to one meaning of the word.