"Introduction to matrices: Groups of matrices, Groups of matrices as metric spaces, Matrixgroups, Some examples of matrix groups, Complex matrix groups as real matrix groups, Continuous homomorphisms of matrix groups, Continuous group actions, The matrix exponential and logarithm functions. Lie algebras for matrix groups: Differential equations in matrices, One parameter subgroups, Curves, tangent spaces and Lie algebras, Some Lie algebras of matrix groups, SO (3) and SU (2) , SL2(C) and the Lorentz group. Quaternions, Clifford algebras and some associated groups: Algebras, Linear algebra over a division algebra, Quaternions, Quaternionic matrix groups, The real Clifford algebras, The spinor groups, Thecenters of spinor groups, Finite subgroups of spinor groups. Matrix groups as Lie groups: Smooth manifolds, Tangent spaces and derivatives, Liegroups, Some examples of Lie groups, Some useful formula in matrix groups, Matrix groups are Lie groups, Not all Lie groups are matrix groups. Homogeneous spaces: Homogeneous spaces as manifolds, orbits, Projectivespaces, Grassmannians. Connectivity of matrix groups: Connectivity of manifolds, Examples of path-connected matrix groups, The path components of a Lie group, Another connectivity result. Compact connected Lie groups and their maximal tori;Tori, Maximal tori in compact Lie groups, The normalizer and Weyl group of a maximal torus."