If I wanted to learn more about rigorous, non-elementary logic, do you have a recommended resource? I've taken a course in intro level probability theory which covered it generally and another course that built on it lightly but nothing rigorous and I am wooed by how concise things become in a logical form.
A Tour Through Mathematical Logic. You don't have to do any proofs. If you learn Propositional Logic and First Order Logic you'll already have most of the tools to invent the rest.