This course will cover groups and rings. In Artin, Algebra, 2nd edition, we will cover chapter 2, sections 6.7 to 6.11 in chapter 6, sections 7.1 to 7.7 in chapter 7, chapter 11, and chapter 12, time permitting. There is a continuation of this course into second semester, called Math 30820, where we will cover topics from chapter 14 through chapter 16.