Here is a great resource from one of the most influential logicians alive.
Johan van Benthem’s book, Modal Logic for Open Minds, is a wonderfully clear introduction to the new synthesis, bringing ideas from logic, philosophy, computer science, and linguistics.
Here are some notes of mine that might be helpful.
Ben-Ari’s article on semantic tableaux.
I’ve posted a couple of good articles about propositional logic and the use of tableaux in proofs. The first is a great article by Mordechai Ben-Ari called
The second is a set of slides on tableaux from Paolo Liberatore’s course on automated reasoning: