Foundations of Mathematics (2015) [pdf]
A substantial portion of this text appears to be concerned with traditional Zermelo–Fraenkel set theory (and its extensions).I have gradually come to believe that ZF theory has received a disproportionate amount of attention on account of the fact that it serves as the "official" foundations of mathematics, but that it is not an especially beautiful, or useful, structure.I believe that ZF theory is an interesting object, worthy of mathematical study, but _not_ the best candidate for the foundations of mathematics! I am very happy to see that this year's Chauvenet Prize [1] was won by Tom Leinster's "Rethinking set theory", in which he highlights that Lawvere set theory looks like a much better candidate. I cannot do better than recommend you look at Leinster's superb article.[1] MAA, Chauvenet Prize, https://www.maa.org/programs-and-communities/member-communit...[2] Leinster, T., "Rethinking set theory", https://arxiv.org/abs/1212.6543