Course Learning Outcomes:

1. Work with axioms of an abstract group, different examples of finite and infinite groups in geometric, combinatorial and algebraic settings.
2. Work with group action on sets and its orbits, the orbit-stabilizer theorem.
3. Work with homomorphism, automorphism, and isomorphism of groups, as well as all three isomorphism theorems for groups.
4. Work with Lagrange's theorem, Euler's theorem, Fermat's Little theorem, Cauchy's theorem, and their applications.
5. Work with subgroups, generators, cosets, conjugacy classes, quotient groups, as well as examples of these notions in different settings.
6. Work with Sylow theorems and their application.