# Lie groups pre-requisites and reference

What are the minimum pre-requisites in analysis (differential geometry) required to study Lie-groups? And for that material, what are some good references?

I have done basic courses in Metric spaces, Topology, Complex analysis etc. and Linear Algebra and Functional analysis. I also have some knowledge of Curves and surfaces ( $\mathbb{R^3}$ ).

I have to do a reading in Lie groups and, perhaps, later continue with its representation theory. Though it is (probably?) an algebraic study, I would still like to know the role played by Lie groups and algebras in Geometry too.

Ideally I would prefer to have a brief but sufficiently rigorous introduction in Differential geometry so that I may continue with the study of Lie groups without hindrance. For that if there is a reference recommendation then I would be really thankful.If there exist some lecture notes serving this purpose,then that would be great too.)

• i think the following notes of Wolfgang Ziller on Lie groups are exactly what you are looking for! math.upenn.edu/~wziller/math650/LieGroupsReps.pdf – Christos Jan 31 '16 at 13:14
• @Christos It already assumes the stuff I am seeking. There is the relevant bibliography, though it is scattered into a few books . I would prefer somewhere with all the relevant things; e.g some book where I can read all the differential geometry I will need to study Lie groups. – Chiha Bakz Jan 31 '16 at 13:24
• Brian C Hall's Lie Groups/Algebras text gives an introduction to the subject that makes heavy use of linear algebra knowledge. However, if you really want a differential topology/geometry approach to manifolds first, I'd recommend Loring Tu's text on Manifolds as a first stop. – Ben Grossmann Jan 31 '16 at 13:40
• @Omnomnomnom: I had a look at that book (Loring Tu). It seems quite nice and readable. Though it has a lot of material (around 100 pages ) before it comes to Lie groups part. Please migrate your comment to the answers. If I don't stumble across any answer mentioning a more concise text, then this seems like the best candidate for my need. – Chiha Bakz Feb 1 '16 at 17:18
• @ChihaBakz done. I hope you find what you're looking for. – Ben Grossmann Feb 1 '16 at 21:03