1) Sets/Properties
2) Equivalence Relations (how to show something is an equivalence relation)/Classes/Properties
3) Functions/1-1/Onto/Bijection/Properties
4) Groups (how to show something is a group), abelian groups, order of a group, properties of groups, cayley tables, etc.
5) Specific groups like Z_n, U(n), etc.
6) Subgroups (how to show something is a subgroup).
Bonus Topic: Center and centralizer (not necessary for exam 1).