These notes formed the basis for a topics course at Oregon State University in 2016.

Introduction

Section 1: $\SO(2)$

Section 2: $\SO(3)$

Section 3: $\SU(2)$

The Hopf Map

Section 4: $\SO(3,1)$

The Cayley-Dickson Process

The Split Complex Numbers

Section 5: Lie Groups and Lie algebras

Section 6: $\SU(2,\CC')$

Section 7: Representations of $\su(2)$

Section 8: $\su(3)$

Section 9: Adjoint Representation

Section 10: Roots

Section 11: Properties of Roots

Section 12: Dynkin Diagrams