Review of basic Group Theory, Direct sum and direct product of groups, Group Actions, Cayley's Theorem, The Class Equation, Sylow's Theorems (15 lectures)
Review of basic Ring Theory, Properties of Ideals, Prime and Maximal Ideals, Two-sided ideals and Quotient Rings, Chinese Reminder Theorem, Euclidean Domain, Euclidean Algorithm, Principal Ideal Domain, Euclidean Domain is a Principal Ideal Domain, UFD, PID implies UFD. (20 lectures)