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0. Notation. Conventions. How to Use This Book 1. Introduction 2. All You Need to Know about Symmetries, Matrices, and Groups 3. A Primer on Rotations and Rotation Matrices 4. Rotations and Angular Momentum 5. Tensor Bases: Introduction to Spinors 6. The Bilinear Transformation 7. Rotations and SU(2). The Stereographic Projection 8. Projective Representations 9. The Geometry of Rotations 10. The Topology of Rotations 11. The Spinor Representations 12. The Algebra of Rotations: Quaternions 13. Double Groups 14. The Irreducible Representations of SO(3) 15. Examples and Applications 16. Solutions to Problems References Index