During undergrad, I was only exposed to logic in my set theory and theory of computation classes. Any recommendations on good books/textbooks that are good for a relative beginners exploring set theory and type theory?
Chapter 1 of the HoTT book introduces Martin-Lof's dependent type theory, then the rest of the book covers HoTT-specific topics: https://homotopytypetheory.org/book/
That's an entire book that is merely a guide on which other books to read and what to focus on in one's journey of formal logic.
I have started with the most intro book it recommends "How to Prove It : A Structured Approach by Daniel J. Velleman". It seems to be quite similar to whatever text book I used in the class that focused on logic in college. I intend to skip around a bit though as my real goal here is to be able to understand all of this advanced type theory that I keep seeing in the FP/Haskell/Idris world.
This is an exposition of Martin-Lof's dependent type theory: http://www.cs.nott.ac.uk/~psztxa/mgs-17/notes-mgs17.pdf Section 5 is about Homotopy Type Theory (HoTT), a newer type theory that is still being developed.
Chapter 1 of the HoTT book introduces Martin-Lof's dependent type theory, then the rest of the book covers HoTT-specific topics: https://homotopytypetheory.org/book/