Syllabus for Algebra I, B.Math
Basic set theory: Equivalence relations and partitions. Zorn's lemma. Axiom of choice. Principle of induction. Groups, subgroups, homomorphisms. Modular arithmetic, quotient groups, isomorphism theorems. Groups acting on sets. Sylow's theorems. Permutation groups. Semidirect products, Free groups.
D.S. Dummit and R.M. Foote, Abstract Algebra