This presentation, as the title suggests, will go over all of the sets! We will begin with an overview of the Zermelo-Fraenkel axioms. This will build into our first class of sets to work with: the ordinals. We will demonstrate some fun facts about these constructions, and prove the principles of induction and recursion for the ordinals. We then visit the axiom of regularity in ZF more thoroughly, and extend our ideas of transfinite induction and recursion to ∈-induction and recursion. Finally, we take all of these foundations to build up the cumulative hierarchy of sets in ZF.