Suggestion for book on topological group and other topics.

Question

What is a great book where I can find the following topics:

1. Topological groups;

2. Topological properties of orthogonal group $O(n)$;

3. Topological properties of special orthogonal group $SO(n)$; for example $SO(n)$ is compact, path-connected etc.

Thanks!

Answer 1

I think that John Stillwell's Naive Lie Theory would be a good choice.