Hi, it's me, a Russian or Ukrainian (not sure) guy trying to comprehend the semantics of the Russian prefixes and explain it somehow.
The idea came to me when I've tried some other languages: the closely related Slavic ones, English with its phrasal verbs, German with its *many* prefixes and other Indo-Europeans.
Obviously we don't do any math when making derivations, and they often aren't mean the same as combinations of their parts. Also, we, natives, can produce the infinity of new words and understand them as well. So how do I classify the derived words (maybe there's real linguistic classification, idk):
a) Semantically transparent, which origin in the productive paradigms. Every native can grasp their meanings and make them up.
b) Metaphor (or metathesis), which have more literary meanings, according to their paradigms, and more figurative one, yet widely used.
c) Learned, which have no visible (for an average speaker) connection to their components. Ones, you can't explain to a child why they're called so. They're the widely used minority of all the derivations.
And yes, I'm aware that the paradigms aren't formulae, as in Esperanto, rather sets of known words of the same derivational pattern, from which by extension the new ones are produced.
Here is a file with what I got now, the prefixes marked green are described quite good, others are not. I listed under the prefixes only the learned/metaphor derivations. The X stands for a root's meaning. You can edit it if you have any corrections, I'd appreciate it. Also, I'd like to see explanations of other's languages paradigms, and compare them with mine.