**Lecture 1**: The concept of a group in some context.

**Lecture 2**: Subgroups, particular of the additive integers.

**Lecture 3**: Some groups. Isomorphisms and automorphisms.

**Lecture 5**: More actions! Introduction to normal subgroups.

**Lecture 7**: Quotients of sets and groups and an isomorphism theorem.

**Lecture 8**: Yet more quotients, the (acutal) first isomorphism theorem, and introduction to symmetries.

**Lecture 9**: Symmetries of Euclidean space in general.

**Lecture 10**: Symmetries of the plane.

**Lecture 11**: Symmetries of the plane, final chapter.

**Lecture 12**: The wild world of higher dimensional symmetries.

**Lecture 13**: Permutations.

**Lecture 14**: Conjugacy classes.

**Lecture 15**: Conjugacy classes: finishing with the icosahedron, p-groups.

**Lecture 16**: The long march to Sylow, part 1: Cauchy's Theorem.

**Lecture 17**: The ~~long march~~ **quick sprint** to Sylow, part 2: Almost all the Sylow Theorems.

**Lecture 18**: Sylow recap, and some small groups.

**Lecture 19**: Sylow recap, and some tricks.

**Lecture 20**: More Sylow tricks.

**Lecture 21**: Semidirect products.

**Lecture 22**: Field Theory.

**Lecture 23**: Bilinear forms on vector spaces, part 1.

**Lecture 24**: Bilinear forms on vector spaces, part 2.

**Lecture 25**: Matrix groups and finite groups of Lie type.

**Lecture 26**: Matrix groups, Lie algebras, and quasi-legal algebraic differentiation.

**Lecture 27**: Mostly SU(2) and SO(3).