I don’t know if there are any particular topics you’re interested in, or at what level of detail you want them presented, but Knuth’s Surreal Numbers is an example of the sort of book you mean:
B. You mean we’re actually using the New Math to decipher this old
A. I hate to admit it, but that’s what it looks like. Here the first
rule says that every number x is a pair of sets called the left set
xL and the right set xR: x=⟨xL,xR⟩.
B. Hold it, your notation mixes me up. I don’t know what’s a set and what’s a number.