Differential Geometry, Lie Groups, and Symmetric Spaces, Volume 80 (Pure and Applied Mathematics)

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) The present book is intended as a textbook and reference work on three topics in the title. Together with a volume in progress on "Groups and Geometric Analysis" it supersedes my "Differential Geometry and Symmetric Spaces," published in 1962. Since that time several branches of the subject, particularly the function theory on symmetric spaces, have developed substantially. I felt that an expanded treatment might now be useful.