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

And the author is the cutest: https://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
- Chpater 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

- Lie group bibliography | 0, 153, 1
- Lie group | 278, 5k, 72
- Differential geometry | 12, 5k, 73
- Geometry | 0, 7k, 118
- Mathematics | 17, 28k, 633
- Ciro Santilli's Homepage | 262, 218k, 4k

- A single exponential map is not enough to recover a simple Lie group from its algebra | 12
- Lie algebra | 570, 1k, 12
- Lie algebra of the special linear group of degree 2 | 569
- Lie group-Lie algebra correspondence | 56, 244, 6
- The product of a exponential of the compact algebra with that of the non-compact algebra recovers a simple Lie from its algebra | 50