Currently I'm studying differential geometry and PDEs - so I often meet the use of groups. I also studied symmetries methods for solutions of differential equations but the connection between Lie groups and Lie algebras is still not implicit for me.
I am looking for a literature which gives a nice description of group theory (I am especially interested in continuous groups) and necessary covers Lie groups and Lie algebras. Thanks in advance.
I think that Naive Lie Theory is an excellent place to start. Once you find what you want to know in it, it has excellent references for where to continue.