Differential Geometry, Lie Groups, and Symmetric Spaces
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Recommended [here](https://math.stackexchange.com/questions/461029/getting-started-with-lie-groups) as a good introduction to Lie theory:> I would suggest you start with chapter 4 of *An Introduction to Manifolds* by Tu, Then study *Lie Groups, Lie Algebras, and Representations: An Elementary Introduction* by Hall and finally study *Differential Geometry, Lie Groups, and Symmetric Spaces* by Helgason.In addition, someone recomended Stillwell's *Naive Lie Theory* as "a great first introduction". also referenced in Whitman, S.J.'s *[Classical Theorems in Lie Algebra Representation Theory: A Beginner's Approach](http://www.vofoundation.org/sites/default/files/LieAlg15.pdf)* Also in the bibliography of [Gilmore 2008](https://isidore.co/calibre/browse/book/4682)
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