Part I. Basic Ideas and Examples 1. Real and Complex Matrix Groups 1.1 Groups of Matrices 1.2 Groups of Matrices as Metric Spaces 1.3 Compactness 1.4 Matrix Groups 1.5 Some Important Examples 1.6 Complex Matrices as Real Matrices 1.7 Continuous Homomorphisms of Matrix Groups 1.8 Matrix Groups for Normed Vector Spaces 1.O Continuous Group Actions 2. Exponentials, Differential Equations and One-parameter Subgroups 2.1 The Matrix Exponential and Logarithm 2.2 Calculating Exponentials and Jordan Form 2.3 Differential Equations in Matrices 2.4 One-parameter Subgroups in Matrix Groups 2.5 One-parameter Subgroups and Differential Equations 3. Tangent Spaces and Lie Algebras 3.1 LieAlgebras. 3.2 Curves, Tangent Spaces and Lie Algebras …… 4. Algebras, Quaternions and Quaternionic Symplectic Groups 5. Clifford Algebras and Spinor Groups 6. Lorentz Groups Part II. Matrix Groups as Lie Groups 7. Lie Groups 8. Homogeneous Spaces 9. Connectivity of Matrix Groups Part III. Compact Connected Lie Groups and their Classification 10. Maximal Tori in Compact Connected Lie Groups 11. Semi simple Factorisation 12. Roots Systems, Weyl Groups and Dynkin Diagrams Hints and Solutions to Selected Exercises Bibliography Index
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