Originally Posted by **serpicojr**

What topics do you need to know? Basic set relations and operations--subsets, intersections, unions, complements, and the various operations that can be built up out of these. You also need to know how these things interact with one another, for example De Morgan's laws. You should know various constructions: power sets, set exponentiation, products, disjoint unions. A basic understanding of cardinality is important: What does it mean for two sets to have the same size? How big is the union of a bunch of sets? How big is the power set? Understanding ordinals is also important, but less so. At some point in algebra and topology, you'll be interested in using the Axiom of Choice, so knowing a little bit about this is important. And it's important to understand, on some level, the difference between actual sets and mere collections of objects.