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]

[1] https://www.maa.org/press/maa-reviews/browse?field_tags_tid=...

[2] https://www.maa.org/press/maa-reviews/browse?field_tags_tid=...

[3] https://www.maa.org/press/maa-reviews/browse?field_tags_tid=...