One of the best books on Lie Groups is said to be Representations of Compact Lie Groups (Graduate Texts in Mathematics). It is one of the rarer books from the geometric approach, as opposed to the algebraic approach.
A Lie group is a differentiable manifold which is also a group such that the group multiplication (and the map sending to ) is a differentiable map.
Homomorphism of Lie groups
A homomorphism of Lie groups is a differentiable group homomorphism between Lie groups.