What background is needed to self-study/learn lie group? Which do books recommend?

Question

What background is needed to self-study/learn lie group? Which do books recommend?

Answer 1

The obvious two things you need to be familiar with are Differential Geometry and Group Theory since Lie groups are differentiable manifolds and at the same time, groups whose operation and taking inverses are smooth. If I recall correctly, Chavelley's book does not give introductions two these subjects. You could complement this book with e.g. Warner's book, Foundations of Differentiable Manifolds and Lie Groups