I am looking for a book talking about Lie groups and Lie algebras but not in a too abstract way.
In fact I am doing physics and I need to understand the structure of Lie algebras : why are elements of a group exponential of the algebra, why is the Lie group the tangent space etc.
I studied groups representation with the book "HF Jones Group representation and physics" and I am looking for a book like this one but talking about Lie groups & Lie algebra.
To give you an idea, I liked this book because it gave physical motivations before introducing the representations of groups, because it has proof and it is not written in a too abstract way, it has corrected exercices. Also it did some reminder on Algebra, Group theory before starting : it doesn't assume a perfect background before starting. And it goes in a straight way, it doesn't say thousands of theorem but it just expose what is necessary to get the main point.
You might want to check out the textbook Quantum Theory, Groups, and Representations: An Introduction by Peter Woit. The PDF is available on his website:
http://www.math.columbia.edu/~woit/
Maybe also Naive Lie Theory by Stillwell is worth a look:
https://www.amazon.com/Naive-Theory-Undergraduate-Texts-Mathematics/dp/144192681X