Why study matrix groups?
Chapter 1. Matrices
Chapter 2. All matrix groups are real matrix groups
Chapter 3. The orthogonal groups
Chapter 4. The topology of matrix groups
Chapter 5. Lie algebras
Chapter 6. Matrix exponentiation
Chapter 7. Matrix groups are manifolds
Chapter 8. The Lie bracket
Chapter 9. Maximal tori

Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori. The volume is suitable for graduate students and researchers interested in group theory. --- summary provided by publisher