Sylabus
Introduction to group theory: basic axioms and examples homomorphisms a isomorphisms group actions
Subgroups: definitions and examples centralizers and normalizers, stabilizers and kernels cyclic groups and cyclic subgroups subgroup generated by subsets of a group the lattice of subgroups of a group
Quotient groups and homomorphisms: definitions and examples more on cosets and Lagrange's theorem the isomorphism theorems
Direct products: definitions and examples
Introduction to ring theory: basic definitions and examples ring homomorphism and quotient rings properties of ideals