Getting started with Lie Groups

I am looking for some material (e.g. references, books, notes) to get started with Lie Groups and Lie Algebra.

My motivation is that I (eventually) want to understand the theory underpinning papers such as these.

The problem is, I am at the Rumsfeldian stage where I don't know what I don' t know. The wikipedia page makes it clear that I lack several prerequisites in modern geometry.

So, what would be a proposed study path to get to this stage? My background is electronic engineering and am comfortable with associated topics (signal processing, estimation theory, Kalman Filtering, etc.)

I would suggest you start with chapter 4 of An Introduction to Manifolds by Tu, Then study Lie Groups, Lie Algebras, and Representations: An Elementary Introduction by Hall and finally study Differential Geometry, Lie Groups, and Symmetric Spaces by Helgason.

Good luck!

Stillwell: Naive Lie Theory is a great first introduction since it covers the very basics and uses SO(3) and SU(2) as examples. And it gives a sneak-preview of group theory and topology too. Though, more advanced topics such as adjoint representation and left-invariance are not covered.