A lot of people have suggested what are very good paths to learning how electronics work, either from a theoretical approach or a hands-on approach, including such classics as the Forrest Mims, however nothing seems to be what you want - nothing seems to be concise enough, or detailed enough. We might as well point you at Maxwell's equations (
https://en.wikipedia.org/wiki/Maxwell%27s_equations) and be done with it. That is everything you can know about electricity & magnetism, in a few handy equations. A complete description of all electronics.
Take this analogy - Computers can be completely defined by saying "We have things that can store numbers, and things that can process numbers, based on a list of instructions that are also represented by numbers, and that is about it", and that is completely true, and completely describes computing, and completely misses the point of what modern computing is all about.
Trying to find a concise description for basic electronic components with the aim that you then will understand all of electronics because they are all built out of these parts is a fallacy - a bit like how understanding the C programming language will help you understand Huffman coding or DSP math.
Most of the really neat electronics is when people use bland components in inventive ways... so the best way is to learn the basic components, learn the basic formula, build and analyse a few circuits, and look at other people's designs. After a while you will start intuitively seeing the structures you are hoping to find. You will then see things like 'that is a bleed resistor, and can be ignored', 'that transistor is an amplifier, but that one is matching impedance, and that one is acting as a current source', and 'that is a resistor is there to limit current' - and when something doesn't make sense, explore Google or books like "The Art of Electronics" to find and understand it.
Anyhow, that's just my ranting