Here is a classic which is lacking:
The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913.
https://en.wikipedia.org/wiki/Principia_Mathematica
Principia is indeed a classic, but the mathematical maturity required to follow that profoundly foundational approach is considerable. Even for professional mathematics (source: professors of mine who specialized in mathematical logic).
BLL includes several categories on logic, though, which include classics by Kleene, Curry, etc. For instance, "Foundations of mathematics" [1], "Philosophy of mathematics" [2], and "Model theory" [3]
