The author seems to have uploaded the entire book by chapters at: www.physics.drexel.edu/~bob/LieGroups.html

And the author is the cutest: www.physics.drexel.edu/~bob/Personal.html.

Overview:

- Chapter 3: gives a bunch of examples of important matrix Lie groups. These are done by imposing certain types of constraints on the general linear group, to obtain subgroups of the general linear group. Feels like the start of a classification
- Chapter 4: defines Lie algebra. Does some basic examples with them, but not much of deep interest, that is mostl left for Chapter 7
- Chapter 5: calculates the Lie algebra for all examples from chapter 3
- Chapter 6: don't know
- Chapter 7: describes how the exponential map links Lie algebras to Lie groups

- A single exponential map is not enough to recover a simple Lie group from its algebra
- Lie algebra
- Lie algebra exponential covering problem
- Lie algebra of $SL(2)$
- Lie group-Lie algebra correspondence
- The product of a exponential of the compact algebra with that of the non-compact algebra recovers a simple Lie from its algebra