What is a transistor and what does it do? For application
Ex: I have a problem. I want to come up with a circuit to take care of said problem. I start to sit down and think about what I would need to solve said problem with circuitry, and never a transistor crosses my mind. Why? Because I really don't understand their use in terms of creating solutions. I can solder them all day long in kits and projects, but I didn't come up with the solution for that circuit, I'm just soldering-by-the-dots.
I would like to know more about "applied" transistors, not "theoretical" transistors. After all if it "changed the face of electronics as we know it", it's a pretty big hole for me to have in my knowledge base.