I: Sophus Lie. - 1. The Geometrical Origins of Lie's Theory. - 2. Jacobi and the Analytical Origins of Lie's Theory. - 3. Lie's Theory of Transformation Groups 18741893. - II: Wilhelm Killing. - 4. The Background to Killing's Work on Lie Algebras. - >Chapter 5. Killing and the Structure of Lie Algebrass. - III: Élie Cartan. - 6. The Doctoral Thesis of Élie Cartan. - 7. Lie's School & Linear Representations. - 8. Cartan's Trilogy: 191314. - IV: Hermann Weyl. - 9. The Göttingen School of Hilbert. - 10. The Berlin Algebraists: Frobenius & Schur. - 11. From Relativity to Representations. - 12. Weyl's Great Papers of 1925 and 1926. - Afterword. Suggested Further Reading. - References. Published & Unpublished Sources. Language: English