- Historical review
- Informal look
- Concept of a manifold
- Concept of a Lie group
- Matrix exponentials
- Matrix Lie groups
- BCH formula
- Lie algebra and the exponential map
- Lie group - Lie algebra correspondence.
- Subgroups and homogenious spaces.
- Representation of compact Lie groups.
- Hilbert's fifth problem for compact
groups: Von Neumann's theorem.