Ciro Santilli 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