I an undergraduate math student with a decent background in abstract algebra. I am looking forward to studying Lie groups this summer...I want some you to suggest good references for the following topics
Differentiable manifolds; Tangent space. Vector fields; Frobenius theorem; Relation between Lie sub-algebras & Lie subgroups; Cartan’s theorem on closed subgroups; One parameter subgroups; Exponential maps; Adjoint representation; Homogeneous spaces; Compact Lie groups; Symmetric spaces.
It would be great if the book/s covers the topic from a beginner's perspective.