= Lie Groups, Physics, and Geometry by Robert Gilmore (2008)
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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. Feels like the start of a <classification (mathematics)>
* 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>