At the beginning, when defining what types, expressions, contexts, etc. looks like. I use a bunch of BNF (https://en.wikipedia.org/wiki/Backus%E2%80%93Naur_Form). I'm afraid I don't actually know a good introduction to BNF.
The clearest account I know of of the most critical part of my notation, namely inference rules (those things with the big horizontal bars), is in Frank Pfenning's notes for his course on Constructive Logic: http://www.cs.cmu.edu/~fp/courses/15317-f09/lectures/02-natd... (the full course of notes is at http://www.cs.cmu.edu/~fp/courses/15317-f09/schedule.html, but the one I've linked is most relevant)
A lot of the rest of my notation (types like A × B, A → B, expressions like λx.e, the judgment Δ;Γ ⊢ e : A meaning "e has type A in context Δ;Γ", and the inference rules themselves) is borrowed from fairly standard type-theory-of-functional-languages stuff. Standard books to read here are Types and Programming Languages by Benjamin Pierce (https://www.cis.upenn.edu/~bcpierce/tapl/); or Practical Foundations for Programming Languages by Bob Harper (https://www.cs.cmu.edu/~rwh/plbook/book.pdf). Those are pretty heavy books that cover a lot of ground, including stuff that's mostly irrelevant to my work. If you're interested, though, they're a great place to start learning about formal PL theory!
Was there anything else in particular you wanted to know about?
