[markkm]

"The set theory formalism presented here differs from the traditional ZF system"

Do not, I repeat, DO NOT study nonstandard theories before familiarizing yourself with the standard theory. The standard set theory (ZFC) survived for over a century for very, very good reasons. Without an exposure to the accepted standards, you will not be able to tell what is reasonable and what is not in this set of notes.

It should also be noted that the author's field of concentration (geometric analysis) has nothing to do with set theory. A typical mathematician knows very little about axiomatic set theory and is prone to making imprecise statements about it.

[gylterud]

While I agree that one could take caution when studying proposed alternative foundations of mathematics (there are a lot of dysfunctional theories out there, and the link may be one of them for all I know), I think it is unfair to presume incompetence based on the fact that the author has another field as his specialisation. ZFC is also not the one true way, there are many sensible ways to formulate set theory, and even valid criticisms of ZFC.

[jacobolus]

Set theory historically exists to serve analysis.

https://www.youtube.com/watch?v=hBcWRZMP6xs