Set Theory: An Open Introduction

This book is a brief introduction to the philosophy of set theory. It is written for students with a little background in logic, and some high school mathematics, aims to scratch the tip of the surface of the philosophy of set theory. By the end of this book, students reading it might have a sense of:

why set theory came about;how to reduce large swathes of mathematics to set theory + arithmetic;how to embed arithmetic in set theory;what the cumulative iterative conception of set amounts to;how one might try to justify the axioms of ZFC.