Lie Groups, a Fantastic book by Daniel Bump
published by Springer Press 2013
This is a graduate math level text. Concise with lots of proofs. The chapters are short enough to read in one sitting. Chapter 7 goes over that a Lie group is a differential manifold.
I was asked to look for books on this topic. It was challenging to search for material with this title. This was the best book that I could find.
I look forward to exploring this topic further.